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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Each integral represents the volume of a solid. Describe the solid.

0 π / 2 2 π ( x + 1 ) ( 2 x sin x )   d x

To determine

To describe:

The solid

Explanation

1) Concept:

 By the shell method the volume of the solid by rotating the region under the curve y=f(x) about the line x=-1 from a to b is

V= ab2π x+1 f(x)dx

where  0ab

2) Given:

0π22π x+1(2x-sinx)dx

3) Calculations:

The volume of the solid is

0π22πx+12x-sinx dx

The volume of the solid obtained by the revolution curve y=fx0 around the line x=  axis in the interval (a, b) is

0π22π x-l2x-sinx dx

Comparing this volume with V= ab2π x+1f

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