Chapter 5.5, Problem 32E

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

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**Writing Integrals** In Exercises 31-34, use a graphing utility to graph the region bounded by the graphs of the functions. Write the definite integral that represents the area of the region. *(Hint:* More than one integral may be necessary.)

To determine

**To graph:** The region bounded by the graphs of functions

Explanation

**Given Information:**

The region bounded by the graphs of

**Graph:**

Use Ti-83 calculator to graph the provided region as follows:

Step 1: Press

Step 2: Press “Window” key. Set the viewing window as

Step 3: Press “2^{nd}”, “Trace” and then “5” key to compute intersection point. Press “Enter” key three times. The intersection point of two graphs is found as

Press “2^{nd}”, “Trace” and then “5” key to compute intersection point. Press “Enter” key two times. Scroll near to second intersection point and press “Enter.” The second intersection point of two graphs is found as

Press “2^{nd}”, “Trace” and then “5” key to compute intersection point. Press “Enter” key two times. Scroll near to third intersection point and press “Enter.” The third intersection point of two graphs is found as

Step 4: Press “2^{nd}”, “Mode”, “2^{nd}” and then “PRGM” key to open “Draw” menu. Scroll to “7:Shade” and press “Enter.”

Step 5: Press “Vars” key, scroll to right and press “Enter” key to open “Functions.” Scroll to “

The graph will be shown as follows:

Step 6: Press “2^{nd}”, “Mode”, “2^{nd}” and then “PRGM” key to open “Draw” menu. Scroll to “7:Shade” and press “Enter.”

Step 7: Press “Vars” key, scroll to right and press “Enter” key to open “Functions.” Scroll to “

The required region will be shown as follows:

**Formula used:**

Area of a region bounded by two graphs is calculated using the following formula,

If *f* and *g* are continuous on *x* in *f*, *g*,

**Calculation:**

From the above, the required area consists of two regions. First region is the area bounded by the graphs of

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