Chapter 5.1, Problem 10E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to *x *or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.

To determine

**To sketch:**

The region enclosed by the given curve and find the area of the region.

Explanation

**1) Concept:**

i. The intersection of two curves is obtained by solving the simultaneous equation of the curves.

ii. Identify the top and the bottom boundaries of region.

iii. Formula-

The area of the typical rectangle is

The total area is

**2) Given:**

3) **Calculation:**

The given curves are

First, find the intersection of these two curves by solving the simultaneous equation.

That is

The graph of the region enclosed by the given curve is

Find the area by integrating with respect to

From graph, the top and the bottom curves are

The graph with the typical rectangle is

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