Explanation 1) Concept: i. If the cross section is a washer with inner radius r i n and outer radius r o u t , then area of washer is obtained by subtracting the area of the inner disk from the area of the outer disk, A = π o u t e r r a d i u s 2 - π i n n e r r a d i u s 2 ii. The volume of the solid revolution about the x -axis is V = ∫ a b A ( x ) d x 2) Given: π ∫ 1 4 3 2 - 3 - x 2 d x 3) Calculation: Compare the given integral with expression for volume. Thus we see that the cross section of the solid of volume the integral represents, is a washer with outer radius 3 and inner radius 3 - x , and it is perpendicular to x - axis. So the axis of rotation is x-axis So, the resulting solid is obtained by rotating the area bounded by the line y = 3 and the curve y = 3 - x and it lies between x = 1 and x = 4 , about the x-axis

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Author: James Stewart

Publisher: Cengage Learning

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Chapter 5.2, Problem 42E

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The solid for an integral π∫1432-3-x2dx which represents the volume of a solid

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Chapter 5.2, Problem 41E

Chapter 5.2, Problem 43E

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The solid for an integral π ∫ 1 4 3 2 - 3 - x 2 d x which represents the volume of a solid

Solution Summary: The author compares the integral with the expression for volume. The cross section of the solid represents a washer with outer and inner radius.

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To describe:

The solid for an integral π∫1432-3-x2dx which represents the volume of a solid

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Chapter 5 Solutions

The solid for an integral π ∫ 1 4 3 2 - 3 - x 2 d x which represents the volume of a solid

Solution Summary: The author compares the integral with the expression for volume. The cross section of the solid represents a washer with outer and inner radius.

Videos

To describe: The solid for an integral π∫1432-3-x2dx which represents the volume of a solid

Want to see the full answer?

Chapter 5 Solutions

To describe:

The solid for an integral π∫1432-3-x2dx which represents the volume of a solid