Chapter 15.2, Problem 31E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the given solid.

**31.** Bounded by the cylinder *x*^{2} + *y*^{2} = 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

The planes are,

**Formula used:**

The volume of the solid,

**Calculation:**

The given plane can be expressed as
*y* varies from 0 and
*x* varies from 0 to 1. Thus, the volume of the solid is computed as follows.

First, compute the integral with respect to *y*.

Apply th

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