Chapter 15.2, Problem 36E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the solid by subtracting two volumes.

**36.** The solid enclosed by the parabolic cylinder *y = x*^{2} and the planes *z* = 3*y*, *z* = 2 + *y*

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,

Two planes intersect at *y =* 1.

Thus, *x* varies from *âˆ’*1 to 1 and *y* varies from

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

First, compute the integral with respect to *y*

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