BuyFind*arrow_forward*

11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 15, Problem 4PS

Textbook Problem

1 views

**Moments of Inertia** Using the formulas from Exercise 3, find the moments of inertia for a wire of density

(see figure).

To determine

**To calculate:** The moment of inertia for a wire given by a curve

**Given:** density of wire

The wire is given by the curve,

And,

density of wire,

**Formula used:**

The moment of inertia about *x*-, *y*-, and *z*-axes are given by,

**Calculation:**

Consider the given curve,

Differentiate *t*’ to get,

Use the fact that,

That is.,

Now,

The moments of inertia about the *x*-axis is given by

Multivariable Calculus

Show all chapter solutions

Ch. 15.1 - Vector Field Define a vector field in the plane...Ch. 15.1 - CONCEPT CHECK Conservative Vector Field What is a...Ch. 15.1 - Potential Function Describe how to find a...Ch. 15.1 - CONCEPT CHECK Vector Field A vector field in space...Ch. 15.1 - Matching In Exercise 5-8, match the vector field...Ch. 15.1 - Matching In Exercise 5-8, match the vector field...Ch. 15.1 - Matching In Exercise 5-8, match the vector field...Ch. 15.1 - Matching In Exercise 5-8, match the vector field...Ch. 15.1 - Sketching a Vector Field In Exercises 914, find F...Ch. 15.1 - Sketching a Vector Field In Exercises 914, find F...

Ch. 15.1 - Sketching a Vector Field In Exercises 914, find F...Ch. 15.1 - Sketching a Vector Field In Exercises 914, find F...Ch. 15.1 - Sketching a Vector Field In Exercises 914, find F...Ch. 15.1 - Sketching a Vector Field In Exercises 914, find F...Ch. 15.1 - Graphing a Vector Field Using Technology In...Ch. 15.1 - Sketching a Vector Field In Exercises 1518, use a...Ch. 15.1 - Graphing a Vector Field Using Technology In...Ch. 15.1 - Graphing a Vector Field Using Technology In...Ch. 15.1 - Finding a Conservative Vector Field In Exercises...Ch. 15.1 - In Exercises 1928, find the conservative vector...Ch. 15.1 - Finding a Conservative Vector Field In Exercises...Ch. 15.1 - Finding a Conservative Vector Field In Exercises...Ch. 15.1 - Finding a Conservative Vector Field In Exercises...Ch. 15.1 - Finding a Conservative Vector Field In Exercises...Ch. 15.1 - Finding a Conservative Vector Field In Exercises...Ch. 15.1 - In Exercises 1928, find the conservative vector...Ch. 15.1 - Finding a Conservative Vector Field In Exercises...Ch. 15.1 - Finding a Conservative Vector Field In Exercises...Ch. 15.1 - Testing for a Conservative Vector Field In...Ch. 15.1 - Testing for a Conservative Vector Field In...Ch. 15.1 - Testing for a Conservative Vector Field In...Ch. 15.1 - Testing for a Conservative Vector Field In...Ch. 15.1 - Testing for a Conservative Vector Field In...Ch. 15.1 - Testing for a Conservative Vector Field In...Ch. 15.1 - Testing for a Conservative Vector Field In...Ch. 15.1 - Testing for a Conservative Vector Field In...Ch. 15.1 - Finding a Potential Function In Exercises 3744,...Ch. 15.1 - Finding a Potential Function In Exercises 3744,...Ch. 15.1 - Finding a Potential Function In Exercises 3744,...Ch. 15.1 - Finding a Potential Function In Exercises 3744,...Ch. 15.1 - Finding a Potential Function In Exercises 37-44,...Ch. 15.1 - Finding a Potential Function In Exercises 3744,...Ch. 15.1 - Finding a Potential Function In Exercises 3744,...Ch. 15.1 - Finding a Potential Function In Exercises 37-44,...Ch. 15.1 - Finding the Curl of a Vector Field In Exercises...Ch. 15.1 - Finding the Curl of a Vector Field In Exercises...Ch. 15.1 - Finding the Curl of a Vector Field In Exercises...Ch. 15.1 - Finding the Curl of the Vector Field In Exercises...Ch. 15.1 - Finding the Curl of a Vector Field Using...Ch. 15.1 - Finding the Curl of a Vector Field Using...Ch. 15.1 - Finding a Potential Function In Exercises 51-56,...Ch. 15.1 - Finding a Potential Function In Exercises 51-56,...Ch. 15.1 - Finding a Potential Function In Exercises 51-56,...Ch. 15.1 - Finding a Potential Function In Exercises 51-56,...Ch. 15.1 - Finding a Potential Function In Exercises 51-56,...Ch. 15.1 - Finding a Potential Function In Exercises 51-56,...Ch. 15.1 - Finding the Divergence of a Vector Field In...Ch. 15.1 - Finding the Divergence of a Vector Field In...Ch. 15.1 - Finding the Divergence of a Vector Field In...Ch. 15.1 - Finding the Divergence of a Vector Field In...Ch. 15.1 - Finding the Divergence of the Vector Field In...Ch. 15.1 - Finding the Divergence of the Vector Field In...Ch. 15.1 - Finding the Divergence of a Vector Field In...Ch. 15.1 - Finding the Divergence of a Vector Field In...Ch. 15.1 - EXPLORING CONCEPTS Think About It In Exercises...Ch. 15.1 - EXPLORING CONCEPTS Think About It In Exercise...Ch. 15.1 - EXPLORING CONCEPTS Think About It In Exercise...Ch. 15.1 - HOW DO YOU SEE IT? Several representative vectors...Ch. 15.1 - Curl of a Cross Product In Exercises 69 and 70,...Ch. 15.1 - Curl of a Cross Product In Exercises 69 and 70,...Ch. 15.1 - Curl of the Curl of a Vector Field In Exercises 71...Ch. 15.1 - Curl of the Curl of a Vector Field In Exercises 71...Ch. 15.1 - Divergence of a Cross Product In Exercises 73 and...Ch. 15.1 - Divergence of a Cross Product In Exercises 73 and...Ch. 15.1 - Divergence of the Curl of a Vector Field In...Ch. 15.1 - Divergence of the Curl of a Vector Field In...Ch. 15.1 - Proof In parts (a) - (h), prove the property for...Ch. 15.1 - Earths magnetic field A cross section of Earths...Ch. 15.2 - CONCEPT CHECK Line integral What is the physical...Ch. 15.2 - CONCEPT CHECK Orientation of a Curve Describe how...Ch. 15.2 - Finding a Piecewise Smooth Parametrization In...Ch. 15.2 - Finding a Piecewise Smooth Parametrization In...Ch. 15.2 - Finding a Piecewise Smooth Parametrization In...Ch. 15.2 - Finding a Piecewise Smooth Parametrization In...Ch. 15.2 - Finding a Piecewise Smooth Parametrization In...Ch. 15.2 - Finding a Piecewise Smooth Parametrization In...Ch. 15.2 - Evaluating a Line Integral In Exercises 9-12, (a)...Ch. 15.2 - Evaluating a Line Integral In Exercises 9-12, (a)...Ch. 15.2 - Evaluating a Line Integral In Exercises 9-12, (a)...Ch. 15.2 - Evaluating a Line Integral In Exercises 9-12, (a)...Ch. 15.2 - Evaluating a Line Integral In Exercises 1316, (a)...Ch. 15.2 - Evaluating a Line IntegralIn Exercises 1316, (a)...Ch. 15.2 - Evaluating a Line Integral In Exercises 1316, (a)...Ch. 15.2 - Evaluating a Line Integral In Exercises 1316, (a)...Ch. 15.2 - Evaluating a Line Integral In Exercises 17 and 18,...Ch. 15.2 - Evaluating a Line Integral In Exercises 17 and 18,...Ch. 15.2 - Evaluating a Line Integral In Exercises 19-22,...Ch. 15.2 - Evaluating a Line Integral In Exercises 19-22,...Ch. 15.2 - Evaluating a Line Integral In Exercises 19-22,...Ch. 15.2 - Evaluating a Line Integral In Exercises 19-22,...Ch. 15.2 - Mass In Exercises 23 and 24, find the total mass...Ch. 15.2 - Mass In Exercises 23 and 24, find the total mass...Ch. 15.2 - Mass In Exercises 25-28, find the total mass of...Ch. 15.2 - Mass In Exercises 25-28, find the total mass of...Ch. 15.2 - Mass In Exercises 25-28, find the total mass of...Ch. 15.2 - Mass In Exercises 25-28, find the total mass of...Ch. 15.2 - Evaluating a Line Integral of a Vector Field In...Ch. 15.2 - Evaluating a Line Integral of a Vector Field In...Ch. 15.2 - Evaluating a Line Integral of a Vector Field In...Ch. 15.2 - Evaluating a Line Integral of a Vector Field In...Ch. 15.2 - Evaluating a Line Integral of a Vector Field In...Ch. 15.2 - Evaluating a Line Integral of a Vector Field In...Ch. 15.2 - Evaluating a Line Integral of a Vector Field Using...Ch. 15.2 - Evaluating a Line Integral of a Vector Field Using...Ch. 15.2 - Work In Exercises 37-42, find the work done by the...Ch. 15.2 - Work In Exercises 37-42, find the work done by the...Ch. 15.2 - Work In Exercises 37-42, find the work done by the...Ch. 15.2 - Work In Exercises 3742, find the work done by the...Ch. 15.2 - Work In Exercises 37-42, find the work done by the...Ch. 15.2 - Work In Exercises 3742, find the work done by the...Ch. 15.2 - Work In Exercises 43-46, determine whether the...Ch. 15.2 - Work In Exercises 43-46, determine whether the...Ch. 15.2 - Work In Exercises 43-46, determine whether the...Ch. 15.2 - Work In Exercises 43-46, determine whether the...Ch. 15.2 - Evaluating a Line Integral of a Vector Field In...Ch. 15.2 - Evaluating a Line Integral of a Vector Field In...Ch. 15.2 - Demonstrating a Property In Exercises 49-52,...Ch. 15.2 - Demonstrating a Property In Exercises 49-52,...Ch. 15.2 - Demonstrating a Property In Exercises 49-52,...Ch. 15.2 - Demonstrating a Property In Exercises 49-52,...Ch. 15.2 - Evaluating a Line Integral in Differential Form In...Ch. 15.2 - Evaluating a Line Integral in Differential Form In...Ch. 15.2 - Evaluating a Line Integral in Differential Form In...Ch. 15.2 - Evaluating a Line Integral in Differential Form In...Ch. 15.2 - Evaluating a Line Integral in Differential Form In...Ch. 15.2 - Evaluating a Line Integral in Differential Form In...Ch. 15.2 - Evaluating a Line Integral in Differential Form In...Ch. 15.2 - Evaluating a Line Integral in Differential Form In...Ch. 15.2 - Evaluating a Line Integral in Differential Form In...Ch. 15.2 - Evaluating a Line Integral in Differential Form In...Ch. 15.2 - Evaluating a Line Integral in Differential Form In...Ch. 15.2 - Evaluating a Line Integral in Differential Form In...Ch. 15.2 - Lateral Surface Area In Exercises 65-72, find the...Ch. 15.2 - Lateral Surface Area In Exercises 65-72, find the...Ch. 15.2 - Lateral Surface Area In Exercises 65-72, find the...Ch. 15.2 - Lateral Surface Area In Exercises 65-72, find the...Ch. 15.2 - Lateral Surface Area In Exercises 65-72, find the...Ch. 15.2 - Lateral Surface Area In Exercises 65-72, find the...Ch. 15.2 - Lateral Surface Area In Exercises 65-72, find the...Ch. 15.2 - Lateral Surface Area In Exercises 65-72, find the...Ch. 15.2 - Engine Design A tractor engine has a steel...Ch. 15.2 - Building Design The ceiling of a building has a...Ch. 15.2 - Moment of Inertia Consider a wire of density (x,y)...Ch. 15.2 - Moment of Inertia Consider a wire of density (x,y)...Ch. 15.2 - Investigation The top outer edge of a solid with...Ch. 15.2 - Work A particle moves along the path y=x2 from the...Ch. 15.2 - Work Find the work done by a person weighing 175...Ch. 15.2 - Investigation Determine the value of c such that...Ch. 15.2 - Think About It A path C is given by x=t,y=2t where...Ch. 15.2 - Line Integrals Let F(x,y)=2xi+xy2j and consider...Ch. 15.2 - Ordering Surfaces Order the surfaces in ascending...Ch. 15.2 - HOW DO YOU SEE IT? For each of the following,...Ch. 15.2 - True or False? In Exercises 85 and 86, determine...Ch. 15.2 - True or False? In Exercises 85 and 86, determine...Ch. 15.2 - Work Consider a particle that moves through the...Ch. 15.3 - CONCEPT CHECK Fundamental Theorem of Line...Ch. 15.3 - Independence of Path What does it mean for a line...Ch. 15.3 - Line Integral of a Conservative Vector Field In...Ch. 15.3 - Line Integral of a Conservative Vector Field In...Ch. 15.3 - Line Integral of a Conservative Vector Field In...Ch. 15.3 - Line Integral of a Conservative Vector Field In...Ch. 15.3 - Line Integral of a Conservative Vector Field In...Ch. 15.3 - Line Integral of a Conservative Vector Field In...Ch. 15.3 - In Exercises 918, Using the Fundamental Theorem of...Ch. 15.3 - Using the Fundamental Theorem of Line Integrals....Ch. 15.3 - Using the Fundamental Theorem of Line Integrals In...Ch. 15.3 - Using the Fundamental Theorem of Line Integrals In...Ch. 15.3 - Using the Fundamental Theorem of Line Integrals In...Ch. 15.3 - Using the Fundamental Theorem of Line Integrals In...Ch. 15.3 - Using the Fundamental Theorem of Line Integrals In...Ch. 15.3 - Using the Fundamental Theorem of Line Integrals In...Ch. 15.3 - Using the Fundamental Theorem of Line Integrals In...Ch. 15.3 - Using the Fundamental Theorem of Line Integrals In...Ch. 15.3 - Finding Work in a Conservative Force Field In...Ch. 15.3 - Finding Work in a Conservative Force Field In...Ch. 15.3 - Finding Work in a Conservative Force Field In...Ch. 15.3 - Finding Work in a Conservative Force Field In...Ch. 15.3 - Evaluating a Line Integral In Exercises 23-32,...Ch. 15.3 - Evaluating a Line Integral In Exercises 23-32,...Ch. 15.3 - Evaluating a Line IntegralIn Exercises 2332,...Ch. 15.3 - Evaluating a Line Integral In Exercises 23-32,...Ch. 15.3 - Evaluating a Line Integral In exercises 2332,...Ch. 15.3 - Evaluating a Line Integral In Exercises 23-32,...Ch. 15.3 - Evaluating a Line Integral In exercises 2332,...Ch. 15.3 - Evaluating a Line Integral In exercises 2332,...Ch. 15.3 - Evaluating a Line Integral In exercises 2332,...Ch. 15.3 - Evaluating a Line Integral In exercises 2332,...Ch. 15.3 - Work A stone weighing 1 pound is attached to the...Ch. 15.3 - Work A grappling hook weighing 1 kilogram is...Ch. 15.3 - Work A zip line is installed 50 meters above...Ch. 15.3 - Can you find a path for the zip line in Exercise...Ch. 15.3 - EXPLORING CONCEPTS Think About It Consider...Ch. 15.3 - Work Let F(x, y, z) = a1i+a2j+a3k be a constant...Ch. 15.3 - Using Different Methods Use two different methods...Ch. 15.3 - HOW DO YOU SEE IT? Consider the force field shown...Ch. 15.3 - Graphical Reasoning In Exercises 41 and 42,...Ch. 15.3 - Graphical Reasoning In Exercises 41 and 42,...Ch. 15.3 - True or False? In Exercises 43-46, determine...Ch. 15.3 - True or False? In Exercises 43-46, determine...Ch. 15.3 - True or False? In Exercises 43-46, determine...Ch. 15.3 - True or False? In Exercises 4346, determine...Ch. 15.3 - Harmonic Function A function f is called harmonic...Ch. 15.3 - Kinetic and Potential Energy The kinetic energy of...Ch. 15.3 - Let F(x,y)=yx2+y2ixx2+y2j Show that Nx=My. Let...Ch. 15.4 - CONCEPT CHECK WritingWhat does it mean for a curve...Ch. 15.4 - Green's Theorem Explain the usefulness of Green's...Ch. 15.4 - Integral SignWhat information do you learn from...Ch. 15.4 - AreaDescribe how to find the area of a plane...Ch. 15.4 - Verifying Greens TheoremIn Exercises 58, verify...Ch. 15.4 - Verifying Greens TheoremIn Exercises 58, verify...Ch. 15.4 - Verifying Greens TheoremIn Exercises 58, verify...Ch. 15.4 - Verifying Green's Theorem In Exercises 5-8, verify...Ch. 15.4 - Verifying Greens TheoremIn Exercises 9 and 10,...Ch. 15.4 - Verifying Greens TheoremIn Exercises 9 and 10,...Ch. 15.4 - Evaluating a Line Integral Using Greens TheoremIn...Ch. 15.4 - Evaluating a Line Integral Using Greens TheoremIn...Ch. 15.4 - Evaluating a Line Integral Using Greens TheoremIn...Ch. 15.4 - Evaluating a Line Integral Using Greens TheoremIn...Ch. 15.4 - Evaluating a Line Integral Using Greens TheoremIn...Ch. 15.4 - Evaluating a Line Integral Using Greens TheoremIn...Ch. 15.4 - Evaluating a Line Integral Using Greens TheoremIn...Ch. 15.4 - Evaluating a Line Integral Using Greens Theorem In...Ch. 15.4 - Evaluating a Line Integral Using Greens TheoremIn...Ch. 15.4 - Evaluating a Line Integral Using Greens TheoremIn...Ch. 15.4 - Evaluating a Line Integral Using Greens TheoremIn...Ch. 15.4 - Evaluating a Line Integral Using Greens TheoremIn...Ch. 15.4 - Evaluating a Line Integral Using Greens TheoremIn...Ch. 15.4 - Evaluating a Line Integral Using Greens TheoremIn...Ch. 15.4 - WorkIn Exercises 2528, use Greens Theorem to...Ch. 15.4 - Work In Exercises 25-28, use Greens Theorem to...Ch. 15.4 - Work In Exercises 25-28, use Greens Theorem to...Ch. 15.4 - Work In Exercises 25-28, use Greens Theorem to...Ch. 15.4 - Area In Exercises 29-32, use a line integral to...Ch. 15.4 - Area In Exercises 29-32, use a line integral to...Ch. 15.4 - Area In Exercises 29-32, use a line integral to...Ch. 15.4 - Area In Exercises 2932, use a line integral to...Ch. 15.4 - Using Green's Theorem to Verify a Formula In...Ch. 15.4 - Using Green's Theorem to Verify a Formula In...Ch. 15.4 - Centroid In Exercises 35-38, use the results of...Ch. 15.4 - Centroid In Exercises 35-38, use the results of...Ch. 15.4 - Centroid In Exercises 35-38, use the results of...Ch. 15.4 - Centroid In Exercises 35-38, use the results of...Ch. 15.4 - Area In Exercises 39-42, use the result of...Ch. 15.4 - Area In Exercises 39-42, use the result of...Ch. 15.4 - Area In Exercises 39-42, use the result of...Ch. 15.4 - Area In Exercises 39-42, use the result of...Ch. 15.4 - Maximum Value (a) Evaluate C1y3dx+(27xx3)dy, where...Ch. 15.4 - HOW DO YOU SEE IT? The figure shows a region R...Ch. 15.4 - Greens Theorem: Region with a Hole Let R be the...Ch. 15.4 - Greens Theorem: Region with a Hole Let R be the...Ch. 15.4 - Think About It Let I=Cydxxdyx2+y2 Where C is a...Ch. 15.4 - Think About It For each given path, verify Greens...Ch. 15.4 - Proff (a) Let C be the line segment joining...Ch. 15.4 - Area Use the result of Exercise 49(b) to find the...Ch. 15.4 - Proof In Exercises 51 and 52, prove the identity,...Ch. 15.4 - Proof In Exercises 51 and 52, prove the identity,...Ch. 15.4 - Proof Let F=Mi+Nj, where M and N have continuous...Ch. 15.4 - Find the least possible area of a convex set in...Ch. 15.5 - CONCEPT CHECK Parametric Surface Explain how a...Ch. 15.5 - CONCEPT CHECK Surface Area A surface S is...Ch. 15.5 - Matching In Exercises 3-8, match the vector-valued...Ch. 15.5 - Matching In Exercises 3-8, match the vector-valued...Ch. 15.5 - Matching In Exercises 3-8, match the vector-valued...Ch. 15.5 - Matching In Exercises 3-8, match the vector-valued...Ch. 15.5 - Matching In Exercises 38, match the vector-valued...Ch. 15.5 - Matching In Exercises 3-8, match the vector-valued...Ch. 15.5 - Sketching a Parametric Surface In Exercises 9-12,...Ch. 15.5 - Sketching a Parametric Surface In Exercises 9-12,...Ch. 15.5 - Sketching a Parametric Surface In Exercises 9-12,...Ch. 15.5 - Sketching a Parametric Surface In Exercises 9-12,...Ch. 15.5 - Graphing a Parametric Surface In Exercises 1316,...Ch. 15.5 - Graphing a Parametric Surface In Exercises 1316,...Ch. 15.5 - Graphing a Parametric Surface In Exercises 1316,...Ch. 15.5 - Graphing a Parametric Surface In Exercises 1316,...Ch. 15.5 - Representing a Surface Parametrically In Exercises...Ch. 15.5 - Representing a Surface Parametrically In Exercises...Ch. 15.5 - Representing a Surface Parametrically In Exercises...Ch. 15.5 - Representing a Surface Parametrically In...Ch. 15.5 - Representing a Surface Parametrically In Exercises...Ch. 15.5 - Representing a Surface Parametrically In Exercises...Ch. 15.5 - Representing a Surface Parametrically In Exercises...Ch. 15.5 - Representing a Surface Parametrically In Exercises...Ch. 15.5 - Representing a Surface Parametrically In Exercises...Ch. 15.5 - Representing a Surface Parametrically In Exercises...Ch. 15.5 - Representing a Surface of Revolution...Ch. 15.5 - Representing a Surface of Revolution...Ch. 15.5 - Representing a Surface of Revolution...Ch. 15.5 - Representing a Surface Revolution ParametricallyIn...Ch. 15.5 - Representing a Surface Revolution ParametricallyIn...Ch. 15.5 - Representing a Surface Revolution ParametricallyIn...Ch. 15.5 - Finding a Tangent Plane In Exercises 33-36, find...Ch. 15.5 - Finding a Tangent Plane In Exercises 3336, find an...Ch. 15.5 - Finding a Tangent Plane In Exercises 33-36, find...Ch. 15.5 - Finding a Tangent Plane In Exercises 33-36, find...Ch. 15.5 - Finding Surface Area In Exercises 37-42, find the...Ch. 15.5 - Finding Surface Area In Exercises 37-42, find the...Ch. 15.5 - Finding Surface Area In Exercises 37-42, find the...Ch. 15.5 - Finding Surface Area In Exercises 3742, find the...Ch. 15.5 - Finding Surface Area In Exercises 37-42, find the...Ch. 15.5 - Finding Surface Area In Exercises 37-42, find the...Ch. 15.5 - EXPLORING CONCEPTS Think About It In Exercises...Ch. 15.5 - EXPLORING CONCEPTS Think About It In Exercises...Ch. 15.5 - EXPLORING CONCEPTS Think About It In Exercises...Ch. 15.5 - EXPLORING CONCEPTS Think About It In Exercises...Ch. 15.5 - Representing a Cone Parametrically Show that the...Ch. 15.5 - HOW DO YOU SEE IT? The figures below are graphs of...Ch. 15.5 - Astroidal Sphere An equation of an astroidal...Ch. 15.5 - Different Views of a Surface Use a computer...Ch. 15.5 - Investigation Use a computer algebra system to...Ch. 15.5 - Investigation Consider the function in Exercise...Ch. 15.5 - Surface Area The surface of the dome on a new...Ch. 15.5 - Hyperboloid Find a vector-valued function for the...Ch. 15.5 - Area Use a computer algebra system to graph one...Ch. 15.5 - Surface Area Lei f be a nonnegative function such...Ch. 15.5 - Open-Ended Project The parametric equations...Ch. 15.5 - Mobius Strip The surface shown in the figure is...Ch. 15.6 - CONCEPT CHECK Surface Integral Explain how to set...Ch. 15.6 - CONCEPT CHECK Surface Integral For what conditions...Ch. 15.6 - CONCEPT CHECK Orientation of a Surface Integral...Ch. 15.6 - CONCEPT CHECK Flux What is the physical...Ch. 15.6 - Evaluating a surface Integral In Exercise 58,...Ch. 15.6 - Evaluating a surface Integral In Exercise 58,...Ch. 15.6 - Evaluating a surface Integral In Exercise 58,...Ch. 15.6 - Evaluating a surface Integral In Exercise 58,...Ch. 15.6 - Evaluating a Surface Integral In Exercises 9 and...Ch. 15.6 - Evaluating a Surface Integral In Exercises 9 and...Ch. 15.6 - Evaluating a Surface Integral In Exercises 11 and...Ch. 15.6 - Evaluating a Surface Integral In Exercises 11 and...Ch. 15.6 - Mass In Exercises 13 and 14, find the mass of the...Ch. 15.6 - Mass In Exercises 13 and 14, find the mass of the...Ch. 15.6 - Evaluating a Surface Integral In Exercises15-18,...Ch. 15.6 - Evaluating a Surface Integral In Exercises 15-18,...Ch. 15.6 - Evaluating a Surface Integral In Exercises 15-18,...Ch. 15.6 - Evaluating a Surface Integral In Exercises 15-18,...Ch. 15.6 - Evaluating a Surface Integral In Exercises 19-24,...Ch. 15.6 - Evaluating a Surface Integral In Exercises 19-24,...Ch. 15.6 - Evaluating a Surface Integral In Exercises...Ch. 15.6 - Evaluating a Surface Integral In Exercises 19-24,...Ch. 15.6 - Evaluating a Surface Integral In Exercises 19-24,...Ch. 15.6 - Evaluating a Surface Integral In Exercises 19-24,...Ch. 15.6 - Evaluating a Flux Integral In Exercises 25-30,...Ch. 15.6 - Evaluating a Flux Integral In Exercises 25-30,...Ch. 15.6 - Evaluating a Flux Integral In Exercises 25-30,...Ch. 15.6 - Evaluating a Flux Integral In Exercises 25-30,...Ch. 15.6 - Evaluating a Flux Integral In Exercises 25-30,...Ch. 15.6 - Evaluating a Flux Integral In Exercises 25-30,...Ch. 15.6 - Evaluating a Flux Integral In Exercises 31 and 32,...Ch. 15.6 - Evaluating a Flux Integral In Exercises 31 and 32,...Ch. 15.6 - Flow Rate In Exercises 33 and 34, use a computer...Ch. 15.6 - Flow Rate In Exercises 33-34, use a computer...Ch. 15.6 - Gauss's Law In Exercises 35 and 36, evaluate SENdS...Ch. 15.6 - Gauss's Law In Exercises 35 and 36, evaluate SENdS...Ch. 15.6 - Moments of Inertia In Exercises 37-40, use the...Ch. 15.6 - Moments of Inertia In Exercises 37-40, use the...Ch. 15.6 - Moments of Inertia In Exercises 37-40, use the...Ch. 15.6 - Moments of Inertia In Exercises 37-40, use the...Ch. 15.6 - EXPLORING CONCEPTS Using Different Methods...Ch. 15.6 - HOW DO YOU SEE IT? Is the surface shown in the...Ch. 15.6 - Investigation (a) Use a computer algebra system to...Ch. 15.7 - CONCEPT CHECK Using Different Methods Suppose that...Ch. 15.7 - Classifying a Point in a Vector Field How do you...Ch. 15.7 - Verifying the Divergence Theorem In Exercises 38,...Ch. 15.7 - Verifying the Divergence Theorem In Exercises 38,...Ch. 15.7 - Verifying the Divergence Theorem In Exercises 38,...Ch. 15.7 - Verifying the Divergence Theorem In Exercises 38,...Ch. 15.7 - Verifying the Divergence Theorem In Exercises 38,...Ch. 15.7 - Verifying the Divergence Theorem In Exercises 38,...Ch. 15.7 - Using the Divergence Theorem In Exercises 9-18,...Ch. 15.7 - Using the Divergence Theorem In Exercises 9-18,...Ch. 15.7 - Using the Divergence Theorem In Exercises 9-18,...Ch. 15.7 - Using the Divergence Theorem In Exercises 9-18,...Ch. 15.7 - Using the Divergence Theorem In Exercises 9-18,...Ch. 15.7 - Using the Divergence Theorem In Exercises 9-18,...Ch. 15.7 - Using the Divergence Theorem In Exercises 9-18,...Ch. 15.7 - Using the Divergence Theorem In Exercises 9-18,...Ch. 15.7 - Using the Divergence Theorem In Exercises 9-18,...Ch. 15.7 - Using the Divergence Theorem In Exercises 9-18,...Ch. 15.7 - Classifying a Point In Exercises 19-22, a vector...Ch. 15.7 - Classifying a Point In Exercises 19-22, a vector...Ch. 15.7 - Classifying a Point In Exercises 19-22, a vector...Ch. 15.7 - Classifying a Point In Exercises 19-22, a vector...Ch. 15.7 - Classifying a Point In Exercises 19-22, a vector...Ch. 15.7 - Classifying a Point In Exercises 19-22, a vector...Ch. 15.7 - EXPLORING CONCEPTS Closed Surface What is the...Ch. 15.7 - HOW DO YOU SEE IT? The graph of a vector field F...Ch. 15.7 - Volume (a) Use the Divergence Theorem to verify...Ch. 15.7 - Constant Vector Field For the constant vector...Ch. 15.7 - Volume For the vector field F(x,y,z)=xi+yj+zk,...Ch. 15.7 - Verifying an Identity For the vector field...Ch. 15.7 - Proof In Exercises 31 and 32, prove the identity,...Ch. 15.7 - Proof In Exercises 31 and 32, prove the identity,...Ch. 15.8 - CONCEPT CHECK Stokess Theorem Explain the benefit...Ch. 15.8 - Curl What is the physical interpretation of curl?Ch. 15.8 - Verifying Stokess Theorem In Exercises 3-6, verify...Ch. 15.8 - Verifying Stokess Theorem In Exercises 3-6, verify...Ch. 15.8 - Verifying Stokess Theorem In Exercises 3-6, verify...Ch. 15.8 - Verifying Stokes Theorem In Exercises 3-6, verify...Ch. 15.8 - Using Stokess Theorem In Exercises 716, use...Ch. 15.8 - Using Stokess Theorem In Exercises 716, use...Ch. 15.8 - Using Stokess Theorem In Exercises 716, use...Ch. 15.8 - Using Stokess TheoremIn Exercises 716, use Stokess...Ch. 15.8 - Using Stokess TheoremIn Exercises 716, use Stokess...Ch. 15.8 - Using Stokess TheoremIn Exercises 716, use Stokess...Ch. 15.8 - Using Stokess Theorem In Exercises 7-16, use...Ch. 15.8 - Using Stokess Theorem In Exercises 7-16, use...Ch. 15.8 - Using Stokes Theorem In Exercises 7-16, use Stokes...Ch. 15.8 - Using Stokes Theorem In Exercises 7-16, use Stokes...Ch. 15.8 - Motion of a Liquid In Exercises 17 and 18, the...Ch. 15.8 - Motion of a Liquid In Exercises 17 and 18, the...Ch. 15.8 - EXPLORING CONCEPTS Think About It Let K be a...Ch. 15.8 - HOW DO YOU SEE IT? Let S1 be the portion of the...Ch. 15.8 - Let G(x,y)=(yx2+4y2,xx2+4y2,0). Prove or disprove...Ch. 15 - Sketching a Vector Field In Exercises 1 and 2,...Ch. 15 - Sketching a Vector Field In Exercises 1 and 2,...Ch. 15 - Finding a Conservative Vector Field In Exercises...Ch. 15 - Finding a Conservative Vector Field In Exercises...Ch. 15 - Finding a Conservative Vector Field In Exercises...Ch. 15 - Finding a Conservative Vector Field In Exercises...Ch. 15 - Testing for a Conservative Vector Field In...Ch. 15 - Testing for a Conservative Vector Field In...Ch. 15 - Testing for a Conservative Vector Field In...Ch. 15 - Testing for a Conservative Vector Field In...Ch. 15 - Finding a Potential Function In Exercises 11-18,...Ch. 15 - Finding a Potential Function In Exercises 11-18,...Ch. 15 - Finding a Potential Function In Exercises 11-18,...Ch. 15 - Finding a Potential Function In Exercises 11-18,...Ch. 15 - Finding a Potential Function In Exercises 11-18,...Ch. 15 - Finding a Potential Function In Exercises 11-18,...Ch. 15 - Finding a Potential Function In Exercises 11-18,...Ch. 15 - Finding a Potential Function In Exercises 11-18,...Ch. 15 - Divergence and Curl In Exercises 19-26, find (a)...Ch. 15 - Divergence and Curl In Exercises 19-26, find (a)...Ch. 15 - Divergence and Curl In Exercises 19-26, find (a)...Ch. 15 - Divergence and Curl In Exercises 19-26, find (a)...Ch. 15 - Divergence and Curl In Exercises 19-26, find (a)...Ch. 15 - Divergence and Curl In Exercises 19-26, find (a)...Ch. 15 - Divergence and Curl In Exercises 19-26, find (a)...Ch. 15 - Divergence and Curl In Exercises 19-26, find (a)...Ch. 15 - Evaluating a Line Integral In Exercises 27-30,...Ch. 15 - Evaluating a Line Integral In Exercises 27-30,...Ch. 15 - Evaluating a Line Integral In Exercises 27-30,...Ch. 15 - Evaluating a Line Integral In Exercises 27-30,...Ch. 15 - Evaluating a Line Integral Using Technology In...Ch. 15 - Evaluating a Line Integral Using Technology In...Ch. 15 - Mass In Exercises 33 and 34, find the total mass...Ch. 15 - Mass In Exercises 33 and 34, find the total mass...Ch. 15 - Evaluating a Line Integral of a Vector Field In...Ch. 15 - Evaluating a Line Integral of a Vector Field In...Ch. 15 - Evaluating a Line Integral of a Vector Field In...Ch. 15 - Evaluating a Line Integral of a Vector Field In...Ch. 15 - Work In Exercises 39 and 40, find the work done by...Ch. 15 - Work In Exercises 39 and 40, find the work done by...Ch. 15 - Evaluating a Line Integral in Differential Form In...Ch. 15 - Evaluating a Line Integral in Differential Form...Ch. 15 - Lateral Surface Area In Exercises 43 and44, find...Ch. 15 - Lateral Surface Area In Exercises 43 and44, find...Ch. 15 - Line Integral of a Conservative Vector Field In...Ch. 15 - Line Integral of a Conservative Vector Field In...Ch. 15 - Using the Fundamental Theorem of Line Integrals In...Ch. 15 - Using the Fundamental Theorem of Line Integrals In...Ch. 15 - Using the Fundamental Theorem of Line Integrals in...Ch. 15 - Using the Fundamental Theorem of Line Integrals in...Ch. 15 - Finding Work in a Conservative Force Field In...Ch. 15 - Finding Work in a Conservative Force Field In...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Work In Exercises 59 and 60, use Greens Theorem to...Ch. 15 - Work In Exercises 59 and 60, use Greens Theorem to...Ch. 15 - Area In Exercises 61 and 61, use a line integral...Ch. 15 - Area In Exercises 61 and 62, use a line integral...Ch. 15 - Sketching a Parametric Surface In Exercise 63 and...Ch. 15 - Sketching a Parametric Surface In Exercise 63 and...Ch. 15 - Graphing a Parametric SurfaceIn Exercise 65 and...Ch. 15 - Graphing a Parametric SurfaceIn Exercise 65 and...Ch. 15 - Representing a Surface Parametrically In Exercises...Ch. 15 - Representing a Surface Parametrically In Exercises...Ch. 15 - Representing a Surface of Revolution...Ch. 15 - Representing a Surface of Revolution...Ch. 15 - Finding a Surface Area In Exercises 71 and 72,...Ch. 15 - Finding a Surface Area In Exercises 71 and 72,...Ch. 15 - Evaluating a Surface Integral In Exercises 73 and...Ch. 15 - Evaluating a Surface Integral In Exercises 73 and...Ch. 15 - Mass In Exercises 75 and 76, find the mass of the...Ch. 15 - Mass In Exercises 75 and 76, find the mass of the...Ch. 15 - Evaluating a Surface Integral In Exercises 77 and...Ch. 15 - Evaluating a Surface Integral In Exercises 77 and...Ch. 15 - Evaluating a Flux Integral In Exercises 79 and 80,...Ch. 15 - Evaluating a Flux IntegralIn Exercises 79 and 80,...Ch. 15 - Using the Divergence TheoremIn Exercises 81 and...Ch. 15 - Using the Divergence TheoremIn Exercises 81 and...Ch. 15 - Using Stokess Theorem In Exercises 83 and 84, use...Ch. 15 - Using Stokess Theorem In Exercises 83 and 84, use...Ch. 15 - Motion of a Liquid In Exercises 85 and 86, the...Ch. 15 - Motion of a Liquid In Exercises 85 and 86, the...Ch. 15 - Heat Flux Consider a single heat source located at...Ch. 15 - Heat Flux Consider a single heat source located at...Ch. 15 - Moments of Inertia Consider a wire of density...Ch. 15 - Moments of Inertia Using the formulas from...Ch. 15 - Laplace's Equation Let F(x,y,z)=xi+yj+zk, and let...Ch. 15 - Greens Theorem Consider the line integral...Ch. 15 - Area Use a line integral to find the area bounded...Ch. 15 - Area Use a line integral to find the area bounded...Ch. 15 - Work The force field F(x,y)=(x+y)i+(x2+1)j acts on...Ch. 15 - Work The force field F(x,y)=3x2y2i+2x3yj is shown...Ch. 15 - Area and Work How does the area of the ellipse...Ch. 15 - Verifying Identities (a) Let f and g be scalar...

Find more solutions based on key concepts

Show solutions Finding Rates of Change In Exercises 95-100, find the average rate or change of the function over the given int...

Calculus: Early Transcendental Functions

The area of the parallelogram at the right is:
26

Study Guide for Stewart's Multivariable Calculus, 8th

Horizontal and Vertical Tangency In Exercises 31 and 32, find all points (if any) of horizontal and vertical ta...

Calculus of a Single Variable

In Exercises 7378, determine whether the statement is true or false. If it is true, explain why it is true. If ...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Evaluate the integral. 36. /4/2cot3xdx

Single Variable Calculus

Find an equation of the slant asymptote. Do not sketch the curve. y=4x310x211x+1x23x

Single Variable Calculus: Early Transcendentals

Modeling Data An instructor gives regular 20-point quizzes and 100-point exams in a mathematics course. Average...

Calculus: Early Transcendental Functions (MindTap Course List)

For f(x) = tanh1 2x, f(x) = a) 2(sech1 2x)2 b) 2(sech2 2x)1 c) 214x2 d) 114x2

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Finding Slopes of Lines In Exercises 27-40, find the slope of the line passing through the pair of points. See ...

Calculus: An Applied Approach (MindTap Course List)

Expand each expression in Exercises 122. (2y+3)(y+5)

Applied Calculus

A tank is full of water. Find the work required to pump the water out of the spout. In Exercises 25 and 26 use ...

Calculus: Early Transcendentals

Let a and b be positive numbers with ab. Let a1 be their arithmetic mean and b1 their geometric mean: a1=a+b2b1...

Calculus (MindTap Course List)

Rectangular Coordinates to Polar Coordinates Convert the rectangular coordinates to polar coordinates with r 0...

Precalculus: Mathematics for Calculus (Standalone Book)

Evaluate the surface integral s F dS for the given vector field F and the oriented surface S. In other words, ...

Multivariable Calculus

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluate the limit, if it exists. limx164x16xx2

Single Variable Calculus: Early Transcendentals, Volume I

Exposure to microbial products, especially endotoxin, may have an impact on vulnerability to allergic diseases....

Probability and Statistics for Engineering and the Sciences

In Exercises 27 to 32, use SSS, SAS, ASA, or AAS to prove that the triangles are congruent. Given: ABBC and ABB...

Elementary Geometry For College Students, 7e

Evaluate the expression sin Exercises 116. (2)3

Finite Mathematics

What is the defining characteristic of a repeated-measures or within-subjects research design?

Statistics for The Behavioral Sciences (MindTap Course List)

Set up and solve equations for each of the following business situations.
19. At a recent boat show, Boater’s P...

Contemporary Mathematics for Business & Consumers

In the layout shown, points E, F, and G are tangent points. Determine lengths OA, OB. and OC.

Mathematics For Machine Technology

For Problems 96-104, write a numerical statement to represent the problem. Then simplify the numerical expressi...

Intermediate Algebra

What is the last step in the calculation of (X)2? a. Square each score. b. Add the scores. c. Square the sum of...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Monthly Payments Technology Pro offers a new computer for $1899, including taxes. If you finance the purchase o...

Mathematical Excursions (MindTap Course List)

Solve: 4x2=12

Elementary Technical Mathematics

Find integer bounds for the zeros of each function. Answers can vary. P(x)=6x313x2110x

College Algebra (MindTap Course List)

Ecology: Habitat Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds ...

Understanding Basic Statistics

In Exercises 724, compute the indicated products. [30211201][212120001122]

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercise 3236 use mathematical induction to prove that the given statement is true for all positive integers...

Elements Of Modern Algebra

Sketch the following between x=0 and x=4. y=12xsinx

Trigonometry (MindTap Course List)

SOC A school system has assigned several hundred "chronic and severe underachievers to an alternative education...

Essentials Of Statistics

The area of an equilateral triangle is 1083in2. If the length of each side of the triangle is 123in, find the l...

Elementary Geometry for College Students

A survey of adult Americans who are Internet users carried out in 2016 found that 79% were Facebook users (Soci...

Introduction To Statistics And Data Analysis

10. A firm has total revenues given by
for x units of a product. Find the maximum revenue from sales of that p...

Mathematical Applications for the Management, Life, and Social Sciences

AreaDescribe how to find the area of a plane region bounded by a piecewise smooth simple closed curve that is o...

Calculus (MindTap Course List)

Refer to the KALI problem presented in this section. The quality control manager requested a producers risk of ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Define experimenter bias, demand characteristics, and reactivity, and explain how these artifacts can threaten ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Barrons reported that the average number of weeks an individual is unemployed is 17.5 weeks. Assume that for th...

Statistics for Business & Economics, Revised (MindTap Course List)

To evaluate the effectiveness of a new television commercial, a researcher measures attitudes toward the advert...

Research Methods for the Behavioral Sciences (MindTap Course List)

In Exercises 16-18, give a decimal answer as it appears on your calculator. Do not round off or convert to a di...

Mathematics: A Practical Odyssey

Domestic Airfare. The Global Business Travel Association reported the domestic airfare for business travel for ...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Reminder Round all answer to two decimal places unless otherwise indicated. A Derivative For f(x)=x2, the avera...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Events A and B in a sample space S are independent if, and only if,______.

Discrete Mathematics With Applications

The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the sta...

Essentials Of Statistics For Business & Economics

Use the following information to answer the next six exercise: On average, a clothing store gets 120 customers ...

Introductory Statistics

For the following exercises, write the equation in equivalent logarithmic form. 260. ex=y

Calculus Volume 1

Length of a Rectangle In Exercises 85 and 86, write the length L of the rectangle as a function of y.

College Algebra

In Problems 110 use the improved Eulers method to obtain a four-decimal approximation of the indicated value. F...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)