Chapter 15.1, Problem 40E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the solid enclosed by the surface *z* = *x*^{2} + *xy*^{2} and the planes *z* = 0, *x* = 0, *x* = 5, and *y =* ±2.

To determine

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

Explanation

**Calculation:**

**Formula used:**

The volume of the solid,

**Given:**

The surface is

The planes are

**Calculation:**

Consider the rectangular region as

Then , the volume of the solid is computed as follows.

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

Apply the limit value for *y*,

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