   Chapter 5.R, Problem 22E

Chapter
Section
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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