   Chapter 15.2, Problem 31E

Chapter
Section
Textbook Problem

Find the volume of the given solid.31. Bounded by the cylinder x2 + y2 = 1 and the planes y = z, x = 0, z = 0 in the first octant

To determine

To find: The volume of the solid that is bounded by the cylinders and planes.

Explanation

Given:

The function is z=y .

The planes are, x=0,z=0,x2+y2=1 .

Formula used:

The volume of the solid, V=DzdA , where, z is the given function.

Calculation:

The given plane can be expressed as y=1x2 . It is observed from the given equations of planes that y varies from 0 and 1x2 and x varies from 0 to 1. Thus, the volume of the solid is computed as follows.

V=RzdA=0101x2ydydx

First, compute the integral with respect to y.

V=01[x22]01x2dx

Apply th

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