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10th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285057095

Chapter 15, Problem 60RE

Textbook Problem

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Verifying Stokes's Theorem In Exercises 59 and 60, verify Stokes’s Theorem by evaluating

as a line integral and as a double integral.

To determine

**To calculate:** The work done by the force *C*: boundary of the region lying between the graphs of

**Given:**

The force is *C*: boundary of the region lying between the graphs of

**Formula used:**

Integration of *x* is given as,

Partial derivative of *x* is given as,

Work done by the force **F** is given by,

**Calculation:**

Consider the provided force,

Compare the force with

Thus,

And,

Thus,

And,

The path *C* is shown below in the figure,

Apply Green’s Theorem and use the value of

It can be seen from the graph that the graphs of

Calculus

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Electrical Charge Let E = xi + yj + 2zk be an...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 - 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 - Classifying a Point in a Vector Field How do you...Ch. 15.7 - 57095-15.7-1E-Question-Digital.docx Verifying the...Ch. 15.7 - Verifying the Divergence Theorem In Exercises 1–6,...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 - 57095-15.7-17E-Question-Digital.docx Using the...Ch. 15.7 - Using the Divergence Theorem In Exercises 17 and...Ch. 15.7 - 57095-15.7-19E-Question-Digital.docx WRITING ABOUT...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 - Finding the Curl of a Vector Field In Exercises...Ch. 15.8 - Finding the Curl of a Vector Field In Exercises...Ch. 15.8 - Finding the Curl of a Vector Field In Exercises...Ch. 15.8 - Finding the Curl of a Vector Field In Exercises...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 Stokes's Theorem In Exercises 9–18, 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 19 and 20, the...Ch. 15.8 - Motion of a Liquid In Exercises 19 and 20, the...Ch. 15.8 - 23. Proof Let C be a constant vector. Let S be an...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 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 In Exercises 21–26,...Ch. 15 - 57095-15-26RE-Question-Digital.docx Evaluating a...Ch. 15 - Evaluating a Line Integral Using Technology In...Ch. 15 - Evaluating a Line Integral Using Technology In...Ch. 15 - Lateral Surface Area In Exercises 43 and44, find...Ch. 15 - Lateral Surface Area In Exercises 43 and44, find...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 - 57095-15-35RE-Question-Digital.docx Evaluating a...Ch. 15 - Evaluating a Line Integral of a Vector Field In...Ch. 15 - 57095-15-37RE-Question-Digital.docx Evaluating a...Ch. 15 - 57095-15-38RE-Question-Digital.docx Evaluating a...Ch. 15 - 57095-15-39RE-Question-Digital.docx Work Find the...Ch. 15 - 57095-15-40RE-Question-Digital.docx Work A 20-ton...Ch. 15 - 57095-15-41RE-Question-Digital.docx Using the...Ch. 15 - 57095-15-42RE-Question-Digital.docx Using the...Ch. 15 - 43. Evaluating a Line Integral Evaluate the line...Ch. 15 - 57095-15-44RE-Question-Digital.docx Area and...Ch. 15 - 57095-15-45RE-Question-Digital.docx Evaluating a...Ch. 15 - Evaluating a Line Integral In Exercises 45–50, use...Ch. 15 - 57095-15-47RE-Question-Digital.docx Evaluating a...Ch. 15 - 57095-15-48RE-Question-Digital.docx Evaluating a...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Graphing a Parametric SurfaceIn Exercise 65 and...Ch. 15 - Graphing a Parametric SurfaceIn Exercise 65 and...Ch. 15 - 57095-15-53RE-Question-Digital.docx Investigation...Ch. 15 - 57095-15-54RE-Question-Digital.docx Evaluating a...Ch. 15 - 57095-15-55RE-Question-Digital.docx Approximating...Ch. 15 - 57095-15-56RE-Question-Digital.docx Mass A...Ch. 15 - Verifying the Divergence Theorem In Exercises 57...Ch. 15 - Verifying the Divergence Theorem In Exercises 57...Ch. 15 - 57095-15-59RE-Question-Digital.docx Verifying...Ch. 15 - 57095-15-60RE-Question-Digital.docx Verifying...Ch. 15 - 57095-15-61RE-Question-Digital.docx Proof Prove...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 - 57095-15-11PS-Question-Digital.docx Proof Let S be...Ch. 15 - Area and Work How does the area of the ellipse...Ch. 15 - Verifying Identities (a) Let f and g be scalar...

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