Chapter 15.2, Problem 34E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the approximate volume of the solid in the first octant that is bounded by the planes *y* = *x, z* = 0, and *z* = *x* and the cylinder *y* = cos *x.* (Use a graphing device to estimate the points of intersection.)

To determine

**To estimate:** The *x*-coordinate of the point of intersection of the curves and evaluate the double integral.

Explanation

**Given:**

The surface is

The curves are

**Formula used:**

The value of the given double integral is,

**Calculation:**

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

The *x*-coordinates of the point of intersection of two curves is at approximately

The value of the given double integral is,

Integrate with respect to *y* and apply the limit.

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