Chapter 15.2, Problem 30E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the given solid.

**30.** Bounded by the cylinder *y*^{2} + *z*^{2} = 4 and the planes *x* = 2*y*, *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 function can be rewritten as
*y* varies from 0 and 2 and *x* varies from 0 to 2*y*. Thus, the volume of the solid is computed as follows.

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

Apply the limit value for *x*,

Compute the integral with respect to *y*

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