Chapter 15.1, Problem 44E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Graph the solid that lies between the surface *z* = 2*xy/(x*^{2} + 1) and the plane *z* = *x +* 2*y* and is bounded by the planes *x* = 0, *x* = 2, *y* = 0, and *y* = 4. Then find its volume.

To determine

**To sketch:** The graph of the given solid that lies between the given surface and the plane and is bounded by the planar region; also find the volume of the solid.

Explanation

**Formula used:**

If

The volume of the solid,

Here,

**Given:**

The surface is

The planes are

**Calculation:**

Let

Then the given solid lies below the surface

Use online graphing calculator and sketch the required graph as shown below in Figure 1.

The rectangular region is

Obtain the volume of the solid by using the equation (1).

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