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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

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

0 4 2 π ( 6 y ) ( 4 y y 2 )   d y

To determine

To describe:

The solid given by the integral

Explanation

1) Concept:

The volume of a solid by rotating the region under the curve  x=g(y) about the line y=l from a to b is

V= ab(2π(l-y)g(y))dy

2) Given:

042π6-y4y-y2dy

3) Calculation:

It is given that the volume of a solid is

042π6-y4y-y2dy 

The volume of the solid obtained by revolution  ofcurve x=gy0 around the line  y=l in the interval ayb   is

V= ab(2π(l-y)g(y))dy

Comparing this volume with 042π6-y4y-y2dy

042

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