Chapter 15.2, Problem 24E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the given solid.

**24.** Under the surface *z* = 1+ *x*^{2}*y*^{2} and above the region enclosed by *x* = *y*^{2} and *x* = 4

To determine

**To find:** The volume of the solid that lies under the surface and above the region *D.*

Explanation

**Given:**

The surface is

The region *D* is,

**Formula used:**

The volume of the solid,

**Calculation:**

Solve both the equation of the region *D* and obtain *y = âˆ’*2 and 2. 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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