Chapter 15.2, Problem 29E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the given solid.

**29.** Enclosed by the cylinders *z* = *x*^{2}*, y* = *x*^{2} and the planes *z* = 0, *y* = 4

To determine

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

Explanation

**Given:**

The function is

The planes are,

The cylinder is

**Formula used:**

The volume of the solid,

**Calculation:**

It is observed from the given equations of planes and cylinders that *y* varies from
*x* varies from *âˆ’*2 to 2. Thus, the volume of the solid is computed as follows.

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

Apply the limit value for *y*,

Compute the integral with respect to *x*

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