Chapter 15.2, Problem 38E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the solid by subtracting two volumes.

**38.** The solid in the first octant under the plane *z* = *x* + *y,* above the surface *z* = *xy,* and enclosed by the surfaces *x =* 0, *y* = 0, and *x*^{2} + *y*^{2} = 4

To determine

**To find:** The volume of the solid that lies in between a plane and a surface.

Explanation

**Given:**

The plane and surface is respectively

The Surfaces enclosed are,

**Formula used:**

The volume of the solid,

**Calculation:**

Express the given plane equation as follows:

And,

From the equation of the circle given, it is observed that *x* varies from âˆ’0 to 2 and *y* varies from 0 to

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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