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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275361

Chapter 7.2, Problem 15E

Textbook Problem

Finding the Volume of a Solid In Exercises 13-16, find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines.

(a) the x-axis

(b) the line

Calculus of a Single Variable

Ch. 7.1 - CONCEPT CHECK Area What is the geometric...Ch. 7.1 - CONCEPT CHECK Area Describe how to find the area...Ch. 7.1 - CONCEPT CHECK Area Between Intersecting Curves...Ch. 7.1 - CONCEPT CHECK Sketching a Region Sketch a region...Ch. 7.1 - Writing a Definite Integral In Exercises 5-10,...Ch. 7.1 - Writing a Definite Integral In Exercises 5-10,...Ch. 7.1 - Writing a Definite Integral In Exercises 5-10,...Ch. 7.1 - Writing a Definite Integral In Exercises 5-10,...Ch. 7.1 - Writing a Definite Integral In Exercises 510,...Ch. 7.1 - Writing a Definite Integral In Exercises 5-10,...

Ch. 7.1 - Finding a Region In Exercises 11-14, the integrand...Ch. 7.1 - Finding a Region In Exercises 11-14, the integrand...Ch. 7.1 - Finding a Region In Exercises 1114, the integrand...Ch. 7.1 - Finding a Region In Exercises 1114, the integrand...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Comparing Methods In Exercises 29 and 30, find the...Ch. 7.1 - Comparing Methods In Exercises 29 and 30, find the...Ch. 7.1 - Finding the Area of a Region In Exercises 31-36,...Ch. 7.1 - Finding the Area of a Region In Exercises 31-36,...Ch. 7.1 - Finding the Area of a Region In Exercises 31-36,...Ch. 7.1 - Finding the Area of a Region In Exercises 31-36,...Ch. 7.1 - Finding the Area of a Region In Exercises 31-36,...Ch. 7.1 - Finding the Area of a Region In Exercises 31-36,...Ch. 7.1 - Finding the Area of a Region In Exercises 37-42,...Ch. 7.1 - Finding the Area of a Region In Exercises 37-42,...Ch. 7.1 - Finding the Area of a Region In Exercises 37-42,...Ch. 7.1 - Finding the Area of a Region In Exercises 37-42,...Ch. 7.1 - Finding the Area of a Region In Exercises 37-42,...Ch. 7.1 - Finding the Area of a Region In Exercises 37-42,...Ch. 7.1 - Finding the Area of a Region In Exercises 43-46,...Ch. 7.1 - Finding the Area of a Region In Exercises 43-46,...Ch. 7.1 - Finding the Area of a Region In Exercises 43-46,...Ch. 7.1 - Finding the Area of a Region In Exercises 43-46,...Ch. 7.1 - Finding the Area of a Region In Exercises 47-50,...Ch. 7.1 - Finding the Area of a Region In Exercises 47-50,...Ch. 7.1 - Finding the Area of a Region In Exercises 47-50,...Ch. 7.1 - Finding the Area of a Region In Exercises 47-50,...Ch. 7.1 - Finding the Area of a Region Find the area of the...Ch. 7.1 - Finding the Area of a Region Find the area of the...Ch. 7.1 - Integration as an Accumulation Process In...Ch. 7.1 - Integration as an Accumulation Process In...Ch. 7.1 - Integration as an Accumulation Process In...Ch. 7.1 - Integration as an Accumulation Process In...Ch. 7.1 - Finding the Area of a Figure In Exercises 57-60,...Ch. 7.1 - Finding the Area of a FigureIn Exercises 57-60,...Ch. 7.1 - Finding the Area of a Figure In Exercises 57-60,...Ch. 7.1 - Finding the Area of a Figure In Exercises 57-60,...Ch. 7.1 - Using a Tangent Line In Exercises 61-64, write and...Ch. 7.1 - Using a Tangent Line In Exercises 61-64, write and...Ch. 7.1 - Using a Tangent Line In Exercises 61-64, write and...Ch. 7.1 - Using a Tangent Line In Exercises 61-64, write and...Ch. 7.1 - EXPLORING CONCEPTS Area Between Curves The graphs...Ch. 7.1 - EXPLORING CONCEPTS Using Symmetry The area of the...Ch. 7.1 - EXPLORING CONCEPTS Interpreting Integrals Two cars...Ch. 7.1 - HOW DO YOU SEE IT? A state legislature is debating...Ch. 7.1 - Dividing a Region In Exercises 69 and 70, find b...Ch. 7.1 - Dividing a Region In Exercises 69 and 70, find b...Ch. 7.1 - Dividing a Region In Exercises 71 and 72, find a...Ch. 7.1 - Dividing a Region In Exercises 71 and 72, find a...Ch. 7.1 - Limits and Integrals In Exercises 73 and 74,...Ch. 7.1 - Limits and Integrals In Exercises 73 and 74,...Ch. 7.1 - Revenue In Exercises 75 and 76, two models R1 and...Ch. 7.1 - Revenue In Exercises 75 and 76, two models R1 and...Ch. 7.1 - Lorenz Curve Economists use Lorenz curves to...Ch. 7.1 - Profit The chief financial officer of a company...Ch. 7.1 - Building Design Concrete sections for a new...Ch. 7.1 - Mechanical Design The surface of a machine part is...Ch. 7.1 - Area Find the area between the graph of y=sinx and...Ch. 7.1 - Area Let a0 and b0. Show that the area of the...Ch. 7.1 - True or False? In Exercises 83-86, determine...Ch. 7.1 - True or False? In Exercises 83-86, determine...Ch. 7.1 - True or False? In Exercises 83-86, determine...Ch. 7.1 - True or False?In Exercises 83-86, determine...Ch. 7.1 - The horizontal line y=c intersects the curve...Ch. 7.2 - CONCEPT CHECK Disk Method Explain how to use the...Ch. 7.2 - CONCEPT CHECK Comparing Methods What is the...Ch. 7.2 - CONCEPT CHECK Finding the Volume of a Solid In...Ch. 7.2 - CONCEPT CHECK Finding the Volume of a Solid...Ch. 7.2 - Finding the Volume of a Solid In Exercises 58,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 58,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 58,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 5-8,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 912,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 912,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 912,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 912,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 13-16,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 13-16,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 13-16,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 13-16,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 1720,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 17-20,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 17-20,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 17-20,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 21-24,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 21-24,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 21-24,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 21-24,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 25-32,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 25-32,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 25-32,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 25-32,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 25-32,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 25-32,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 25-32,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 25-32,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 33-36,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 33-36,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 33-36,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 33-36,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 37-40,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 37-40,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 37-40,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 37-40,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 4148,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 41-48,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 41-48,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 41-48,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 41-48,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 41-48,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 41-48,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 41-48,...Ch. 7.2 - Finding the Volume of a Solid Using Technology In...Ch. 7.2 - Finding the Volume of a Solid Using Technology In...Ch. 7.2 - Finding the Volume of a Solid Using Technology In...Ch. 7.2 - Dividing a SolidIn Exercises 57 and 58, consider...Ch. 7.2 - Dividing a SolidIn Exercises 57 and 58, consider...Ch. 7.2 - Manufacturing For the metal sphere in Exercises...Ch. 7.2 - Volume of a Fuel Tank A tank on the wing of a jet...Ch. 7.2 - Volume of a Container A container can be modeled...Ch. 7.2 - Finding Volumes of Solids Find the volumes of the...Ch. 7.2 - Minimum Volume The function y=4(x2/4) on the...Ch. 7.2 - Modeling Data A draftsman is asked to determine...Ch. 7.2 - Cavalieris Theorem Prove that if two solids have...Ch. 7.3 - CONCEPT CHECK Shell Method Explain how to use the...Ch. 7.3 - CONCEPT CHECK Representative Rectangles Compare...Ch. 7.3 - Finding the Volume of a Solid In Exercises 3-12,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 3-12,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 3-12,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 3-12,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 3-12,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 3-12,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 3-12,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 3-12,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 3-12,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 3-12,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 23-26,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 23-26,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 23-26,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 23-26,...Ch. 7.3 - Choosing a Method In Exercises 27 and 28, decide...Ch. 7.3 - Choosing a Method In Exercises 27 and 28, decide...Ch. 7.3 - Choosing a Method In Exercises 29-32, use the disk...Ch. 7.3 - Choosing a Method In Exercises 29-32, use the disk...Ch. 7.3 - Choosing a Method In Exercises 29-32, use the disk...Ch. 7.3 - Choosing a Method In Exercises 29-32, use the disk...Ch. 7.3 - Finding the Volume of a Solid Using Technology In...Ch. 7.3 - Finding the Volume of a Solid Using Technology In...Ch. 7.3 - Finding the Volume of a Solid Using Technology In...Ch. 7.3 - Finding the Volume of a Solid Using Technology In...Ch. 7.3 - EXPLORING CONCEPTS Describing Cylindrical Shells...Ch. 7.3 - EXPLORING CONCEPTS Think About It A solid is...Ch. 7.3 - EXPLORING CONCEPTS Comparing Integrals In...Ch. 7.3 - EXPLORING CONCEPTS Comparing Integrals In...Ch. 7.3 - Comparing Volumes The region in the figure is...Ch. 7.3 - HOW DO YOU SEE IT? Use the graph to answer the...Ch. 7.3 - Analyzing an Integral In Exercises 43-46, the...Ch. 7.3 - Analyzing an Integral In Exercises 43-46, the...Ch. 7.3 - Analyzing an Integral In Exercises 43-46, the...Ch. 7.3 - Analyzing an Integral In Exercises 43-46, the...Ch. 7.3 - Machine Part A solid is generated by revolving the...Ch. 7.3 - Machine Part A solid is generated by revolving the...Ch. 7.3 - Volume of a Torus A torus is formed by revolving...Ch. 7.3 - Volume of a Torus Repeat Exercise 49 for a torus...Ch. 7.3 - Finding Volumes of Solids (a) Use differentiation...Ch. 7.3 - Finding Volumes of Solids (a) Use differentiation...Ch. 7.3 - Volume of a Segment of a Sphere Let a sphere of...Ch. 7.3 - Volume of an Ellipsoid Consider the plane region...Ch. 7.3 - Exploration Consider the region bounded by the...Ch. 7.3 - Think About It Match each integral with the solid...Ch. 7.3 - Volume of a Storage Shed A storage shed has a...Ch. 7.3 - Modeling Data A pond is approximately circular,...Ch. 7.3 - Equal Volumes Let V1 and V2 be the volumes of the...Ch. 7.3 - Volume of a Segment of a Paraboloid The region...Ch. 7.3 - Finding Volumes of Solids Consider the graph of...Ch. 7.4 - CONCEPT CHECK Rectifiable Curve Describe the...Ch. 7.4 - CONCEPT CHECK Arc Length Explain how to find the...Ch. 7.4 - CONCEPT CHECK Arc Length Name a function for which...Ch. 7.4 - CONCEPT CHECK Surface of Revolution Describe a...Ch. 7.4 - Finding Distance Using Two Methods In Exercises 5...Ch. 7.4 - Finding Distance Using Two Methods In Exercises 5...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 720, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 21-30, (a) sketch...Ch. 7.4 - Finding Arc Length In Exercises 21-30, (a) sketch...Ch. 7.4 - Finding Arc Length In Exercises 21-30, (a) sketch...Ch. 7.4 - Finding Arc Length In Exercises 21-30, (a) sketch...Ch. 7.4 - Finding Arc Length In Exercises 21-30, (a) sketch...Ch. 7.4 - Finding Arc Length In Exercises 21-30, (a) sketch...Ch. 7.4 - Finding Arc Length In Exercises 21-30, (a) sketch...Ch. 7.4 - Finding Arc Length In Exercises 21-30, (a) sketch...Ch. 7.4 - Finding Arc Length In Exercises 21-30, (a) sketch...Ch. 7.4 - Finding Arc Length In Exercises 21-30, (a) sketch...Ch. 7.4 - Approximation In Exercises 31 and 32, approximate...Ch. 7.4 - Approximation In Exercises 31 and 32, approximate...Ch. 7.4 - Length of a Cable An electric cable is hung...Ch. 7.4 - Roof Area A barn is 100 feet long and 40 feet wide...Ch. 7.4 - Length of Gateway Arch The Gateway Arch in St....Ch. 7.4 - Astroid Find the total length of the graph of the...Ch. 7.4 - Arc Length of a Sector of a Circle Find the arc...Ch. 7.4 - Arc Length of a Sector of a Circle Find the arc...Ch. 7.4 - Finding the Area of a Surface of Revolution In...Ch. 7.4 - Finding the Area of a Surface of Revolution In...Ch. 7.4 - Finding the Area of a Surface of Revolution In...Ch. 7.4 - Finding the Area of a Surface of Revolution In...Ch. 7.4 - Finding the Area of a Surface of Revolution In...Ch. 7.4 - Finding the Area of a Surface of Revolution In...Ch. 7.4 - Finding the Area of a Surface of Revolution In...Ch. 7.4 - Finding the Area of a Surface of Revolution In...Ch. 7.4 - Finding the Area of a Surface of Revolution In...Ch. 7.4 - Finding the Area of a Surface of Revolution In...Ch. 7.4 - Finding the Area of a Surface of Revolution Using...Ch. 7.4 - Finding the Area of a Surface of Revolution Using...Ch. 7.4 - EXPLORING CONCEPTS Approximation In Exercises 51...Ch. 7.4 - EXPLORING CONCEPTS Approximation In Exercises 51...Ch. 7.4 - EXPLORING CONCEPTS Approximation In Exercises 51...Ch. 7.4 - HOW DO YOU SEE IT? The graphs of the functions f1...Ch. 7.4 - Think About It The figure shows the graphs of the...Ch. 7.4 - Verifying a Formula (a) Given a circular sector...Ch. 7.4 - Lateral Surface Area of a Cone A right circular...Ch. 7.4 - Lateral Surface Area of a Cone A right circular...Ch. 7.4 - Using a Sphere Find the area of the segment of a...Ch. 7.4 - Using a Sphere Find the area of the segment of a...Ch. 7.4 - Modeling Data The circumference C (in inches) of a...Ch. 7.4 - Modeling Data Property bounded by two...Ch. 7.4 - Volume and Surface Area Let R be the region...Ch. 7.4 - Think About It Consider the equation x29+y24=1 (a)...Ch. 7.4 - Approximating Arc Length or Surface Area In...Ch. 7.4 - Approximating Arc Length or Surface Area In...Ch. 7.4 - Approximating Arc Length or Surface Area In...Ch. 7.4 - Approximating Arc Length or Surface Area In...Ch. 7.4 - Suspension Bridge A cable for a suspension bridge...Ch. 7.4 - Suspension Bridge The Humber Bridge, located in...Ch. 7.4 - Arc Length and Area Let C be the curve given by...Ch. 7.4 - PUTNAM EXAM CHALLENGE Find the length of the curve...Ch. 7.5 - CONCEPT CHECK Work How do you know when work is...Ch. 7.5 - CONCEPT CHECK Comparing Methods Describe the...Ch. 7.5 - CONCEPT CHECK Hooke's Law Describe Hookes Law in...Ch. 7.5 - CONCEPT CHECK Work What are two ways to write the...Ch. 7.5 - Constant Force In Exercises 5-8, determine the...Ch. 7.5 - Constant Force In Exercises 5-8, determine the...Ch. 7.5 - Constant Force In Exercises 5-8, determine the...Ch. 7.5 - Constant Force In Exercises 5-8, determine the...Ch. 7.5 - Hooke's Law In Exercises 9-14, use Hookes Law to...Ch. 7.5 - Hooke's Law In Exercises 9-14, use Hookes Law to...Ch. 7.5 - Hooke's Law In Exercises 9-14, use Hookes Law to...Ch. 7.5 - Hooke's Law In Exercises 9-14, use Hookes Law to...Ch. 7.5 - Hooke's Law In Exercises 9-14, use Hookes Law to...Ch. 7.5 - Hooke's Law In Exercises ï¿½-14, use Hookes Law to...Ch. 7.5 - Propulsion Neglecting air resistance and the...Ch. 7.5 - Propulsion Use the information in Exercise 15 to...Ch. 7.5 - Propulsion Neglecting air resistance and the...Ch. 7.5 - Propulsion A lunar module weighs 12 metric tons on...Ch. 7.5 - Pumping Water A rectangular tank with a base 4...Ch. 7.5 - Think About It Explain why the answer in part (b)...Ch. 7.5 - Pumping Water A cylindrical water tank 4 meters...Ch. 7.5 - Pumping Water Suppose the tank in Exercise 21 is...Ch. 7.5 - Pumping Water An open tank has the shape of a...Ch. 7.5 - Pumping Water Water is pumped in through the...Ch. 7.5 - Pumping Water A hemispherical tank of radius 6...Ch. 7.5 - Pumping Diesel Fuel The fuel tank on a truck has...Ch. 7.5 - Pumping Gasoline In Exercises 27 and 28, find the...Ch. 7.5 - Pumping Gasoline In Exercises 27 and 28, find the...Ch. 7.5 - Winding a Chain In Exercises 29-32, consider a...Ch. 7.5 - Winding a Chain In Exercises 29-32, consider a...Ch. 7.5 - Winding a Chain In Exercises 29-32, consider a...Ch. 7.5 - Winding a Chain In Exercises 29-32, consider a...Ch. 7.5 - Lifting a Chain In Exercises 33 and 34, consider a...Ch. 7.5 - Lifting a Chain In Exercises 33 and 34, consider a...Ch. 7.5 - EXPLORING CONCEPTS, Think About It Does it take...Ch. 7.5 - EXPLORING CONCEPTS Think About It In Example 1,...Ch. 7.5 - Newton's Law of Universal Gravitation Consider two...Ch. 7.5 - Conjecture Use Newtons Law of Universal...Ch. 7.5 - Electric Force Two electrons repel each other with...Ch. 7.5 - HOW DO YOU SEE IT? The graphs show the force Fi...Ch. 7.5 - Ordering Forces Verify your answer to Exercise 40...Ch. 7.5 - Comparing Work Order the following from least to...Ch. 7.5 - Boyle's Law In Exercises 43 and 44, find the work...Ch. 7.5 - Boyle's Law In Exercises 43 and 44, find the work...Ch. 7.5 - Hydraulic Press In Exercises 45-48, use the...Ch. 7.5 - Hydraulic Press In Exercises 45-48, use the...Ch. 7.5 - Hydraulic Press In Exercises 45-48, use the...Ch. 7.5 - Hydraulic Press In Exercises 45-48, use the...Ch. 7.5 - Modeling Data The hydraulic cylinder on a...Ch. 7.6 - CONCEPT CHECK Mass and Weight How are mass and...Ch. 7.6 - CONCEPT CHECK Moment The equation for the moment...Ch. 7.6 - CONCEPT CHECK Planar Lamina What is a planar...Ch. 7.6 - CONCEPT CHECK Theorem of Pappus Explain why the...Ch. 7.6 - Center of Mass of a Linear System In Exercises...Ch. 7.6 - Center of Mass of a Linear System In Exercises...Ch. 7.6 - Center of Mass of a Linear System In Exercises...Ch. 7.6 - Center of Mass of a Linear System In Exercises...Ch. 7.6 - Equilibrium of a Linear System In Exercises 9 and...Ch. 7.6 - Equilibrium of a Linear System In Exercises 9 and...Ch. 7.6 - Center of Mass of a Two-Dimensional System In...Ch. 7.6 - Center of Mass of a Two-Dimensional System In...Ch. 7.6 - Center of Mass of a Two-Dimensional System In...Ch. 7.6 - Center of Mass of a Two-Dimensional System In...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Approximating a Centroid Using Technology In...Ch. 7.6 - Approximating a Centroid Using Technology In...Ch. 7.6 - Finding the Center of Mass In Exercises 31-34,...Ch. 7.6 - Finding the Center of Mass In Exercises 31-34,...Ch. 7.6 - Finding the Center of Mass In Exercises 31-34,...Ch. 7.6 - Finding the Center of Mass In Exercises 31-34,...Ch. 7.6 - Finding the Center of Mass Find the center of mass...Ch. 7.6 - Finding the Center of Mass Find the center of mass...Ch. 7.6 - Finding Volume by the Theorem of Pappus In...Ch. 7.6 - Finding Volume by the Theorem of Pappus In...Ch. 7.6 - Finding Volume by the Theorem of Pappus In...Ch. 7.6 - Finding Volume by the Theorem of Pappus In...Ch. 7.6 - EXPLORING CONCEPTS Center of Mass What happens to...Ch. 7.6 - EXPLORING CONCEPTS Centroid Explain why the...Ch. 7.6 - EXPLORING CONCEPTS Center of Mass Use rectangles...Ch. 7.6 - HOW DO YOU SEE IT? The centroid of the plane...Ch. 7.6 - Centroid of a Common Region In Exercises 45-50,...Ch. 7.6 - Centroid of a Common Region In Exercises 45-50,...Ch. 7.6 - Centroid of a Common Region In Exercises 45-50,...Ch. 7.6 - Centroid of a Common Region In Exercises 45-50,...Ch. 7.6 - Centroid of a Common Region In Exercises 45-50,...Ch. 7.6 - Centroid of a Common Region In Exercises 45-50,...Ch. 7.6 - Graphical Reasoning Consider the region bounded by...Ch. 7.6 - Graphical and Numerical Reasoning Consider the...Ch. 7.6 - Modeling Data The manufacturer of glass for a...Ch. 7.6 - Modeling Data The manufacturer of a boat needs...Ch. 7.6 - Second Theorem of Pappus In Exercises 55 and 56,...Ch. 7.6 - Second Theorem of Pappus In Exercises 55 and 56,...Ch. 7.6 - Finding a Centroid Let n1 be constant, and...Ch. 7.6 - Finding a Centroid Consider the functions...Ch. 7.6 - PUTNAM EXAM CHALLENGE Let V be the region in the...Ch. 7.7 - CONCEPT CHECK Fluid Pressure Describe fluid...Ch. 7.7 - CONCEPT CHECK Fluid Pressure Docs fluid pressure...Ch. 7.7 - Force on a Submerged Sheet In Exercises 3-6, the...Ch. 7.7 - Force on a Submerged Sheet In Exercises 36, the...Ch. 7.7 - Force on a Submerged Sheet In Exercises 36, the...Ch. 7.7 - Force on a Submerged Sheet In Exercises 36, the...Ch. 7.7 - Force on a Submerged Sheet In Exercises 7 and 8,...Ch. 7.7 - Force on a Submerged Sheet In Exercises 7 and 8,...Ch. 7.7 - Fluid Force on a Tank Wall In Exercises 9-14, find...Ch. 7.7 - Fluid Force on a Tank Wall In Exercises 914, find...Ch. 7.7 - Fluid Force on a Tank Wall In Exercises 914, find...Ch. 7.7 - Fluid Force on a Tank Wall In Exercises 914, find...Ch. 7.7 - Fluid Force on a Tank Wall In Exercises 914, find...Ch. 7.7 - Fluid Force on a Tank Wall In Exercises 914, find...Ch. 7.7 - Fluid Force of a Water In Exercises 15-18, find...Ch. 7.7 - Fluid Force of Water In Exercises 15-18, find the...Ch. 7.7 - Fluid Force of Water In Exercises 1518, find the...Ch. 7.7 - Fluid Force of Water In Exercises 1518, find the...Ch. 7.7 - Force on a Concrete Form In Exercises 19-22, the...Ch. 7.7 - Force on a Concrete formIn Exercises 1922, the...Ch. 7.7 - Force on a Concrete Form In Exercises 19-22, the...Ch. 7.7 - Force on a Concrete Form In Exercises 19-22, the...Ch. 7.7 - Fluid Force of Gasoline A cylindrical gasoline...Ch. 7.7 - Fluid Force of Gasoline Repeat Exercise 23 for a...Ch. 7.7 - EXPLORING CONCEPTS Fluid Pressure Explain why...Ch. 7.7 - EXPLORING CONCEPTS Buoyant Force Buoyant force is...Ch. 7.7 - EXPLORING CONCEPTS Think About It Approximate the...Ch. 7.7 - HOW DO YOU SEE IT? Two identical semicircular...Ch. 7.7 - Fluid Force on a Circular Plate A circular plate...Ch. 7.7 - Fluid Force on a Circular Plate Use the result of...Ch. 7.7 - Fluid Force on a Rectangular Plate A rectangular...Ch. 7.7 - Fluid Force on a Rectangular Plate Use the result...Ch. 7.7 - Submarine Porthole A square porthole on a vertical...Ch. 7.7 - Submarine Pothole Repeat Exercise 33 for a...Ch. 7.7 - Modeling Data The vertical stern of a boat...Ch. 7.7 - Irrigation Canal Gate The vertical cross section...Ch. 7 - Finding the Area of a RegionIn Exercises 110,...Ch. 7 - Finding the Area of a RegionIn Exercises 1-10,...Ch. 7 - Finding the Area of a RegionIn Exercises 1-10,...Ch. 7 - Finding the Area of a RegionIn Exercises 1-10,...Ch. 7 - Finding the Area of a RegionIn Exercises 1-10,...Ch. 7 - Finding the Area of a RegionIn Exercises 1-10,...Ch. 7 - Finding the Area of a RegionIn Exercises 1-10,...Ch. 7 - Finding the Area of a RegionIn Exercises 1-10,...Ch. 7 - Finding the Area of a Region In Exercises 1-10,...Ch. 7 - Finding the Area of a RegionIn Exercises 1-10,...Ch. 7 - Finding the Area of a Region In Exercises 11-14,...Ch. 7 - Finding the Area of a Region In Exercises 11-14,...Ch. 7 - Finding the Area of a RegionIn Exercises 11-14,...Ch. 7 - Finding the Area of a RegionIn Exercises 11-14,...Ch. 7 - Integration as an Accumulation Process In...Ch. 7 - Integration as an Accumulation Process In...Ch. 7 - Revenue In Exercises 17 and 18, two models R1 and...Ch. 7 - Revenue In Exercises 17 and 18, two models R1 and...Ch. 7 - Finding the Volume of a Solid In Exercises 19 and...Ch. 7 - Finding the Volume of a Solid In Exercises 19 and...Ch. 7 - Finding the Volume of a Solid In Exercises 21 and...Ch. 7 - Finding the Volume of a Solid In Exercises 21 and...Ch. 7 - Finding the Volume of a Solid In Exercises 23 and...Ch. 7 - Finding the Volume of a Solid In Exercises 23 and...Ch. 7 - Gasoline Tank A gasoline tank is an oblate...Ch. 7 - Using Cross Sections Find the volume of the solid...Ch. 7 - Finding Arc Length In Exercises 27 and 28, find...Ch. 7 - Finding Arc Length In Exercises 27 and 28, find...Ch. 7 - Finding the Area of a Surface of Revolution In...Ch. 7 - Finding the Area of a Surface of Revolution In...Ch. 7 - Finding the Area of a Surface of Revolution In...Ch. 7 - Finding the Area of a Surface of Revolution In...Ch. 7 - Hooke's Law A force of 5 pounds stretches a spring...Ch. 7 - Hooke's Law A force of 50 pounds stretches a...Ch. 7 - Propulsion Neglecting air resistance and the...Ch. 7 - Pumping Water A water well has an 8-inch diameter...Ch. 7 - Winding a Chain A chain 10 feet long weighs 4...Ch. 7 - Winding a Cable A 200-foot cable weighing 5 pounds...Ch. 7 - Boyles Law A quantity of gas with an initial...Ch. 7 - Boyles Law A quantity of gas with an initial...Ch. 7 - Center of Mass of a Linear System Find the center...Ch. 7 - Center of Mass of a Two-Dimensional System Find...Ch. 7 - Center of Mass of a Planar Lamina In Exercises 43...Ch. 7 - Center of Mass of a Planar Lamina In Exercises 43...Ch. 7 - Finding the Center of Mass Introduce an...Ch. 7 - Finding Volume Use the Theorem of Pappus to find...Ch. 7 - Force on a Submerged Sheet In Exercises 47 and 48,...Ch. 7 - Force on a Submerged Sheet In Exercises 47 and 48,...Ch. 7 - Fluid Force of Seawater Find the fluid force on...Ch. 7 - Force on a Concrete Form The vertical side of a...Ch. 7 - Submarine Porthole A circular porthole on a...Ch. 7 - Finding a Limit Let R be the area of the region in...Ch. 7 - Center of Mass of a Lamina Let L be the lamina of...Ch. 7 - Dividing a Region Let R be the region bounded by...Ch. 7 - Surface Area Graph the curve 8y2=x2(1x2) Use a...Ch. 7 - Centroid A blade on an industrial fan has the...Ch. 7 - Volume A blade is cut through the center of a...Ch. 7 - Volume A rectangle R of length l and width w is...Ch. 7 - Comparing Areas of Regions (a) The tangent line to...Ch. 7 - Using Arc Length The graph of y=f(x) passes...Ch. 7 - Using a Function Let f be rectifiable on the...Ch. 7 - Archimedes' Principle Archimedes' Principle states...Ch. 7 - Finding a Centroid Sketch the region bounded on...Ch. 7 - Finding a Centroid Sketch the region bounded on...Ch. 7 - Work Find the work done by each force F.Ch. 7 - Consumer and Producer Surplus In Exercises 15 and...Ch. 7 - Consumer and Producer Surplus In Exercises 15 and...Ch. 7 - Fluid Force A swimming pool is 20 feet wide, 40...

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