Chapter 15.2, Problem 35E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the solid by subtracting two volumes.

**35.** The solid enclosed by the parabolic cylinders *y* = 1 − *x*^{2}, *y* = *x*^{2} − 1 and the planes *x* + *y* + *z* = 2, 2*x* + 2*y* − *z* + 10 = 0

To determine

**To find:** The volume of the solid that lies in between two planes.

Explanation

**Given:**

The planes are

The parabolic cylinders are,

**Formula used:**

The volume of the solid,

**Calculation:**

Express the given plane equation as follows:

And,

The parabolas
*x* varies from âˆ’1 to 1 and *y* varies from

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

First, compute the integral with respect to *y*

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