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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

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.)

f ( x ) = 2 x , g ( x ) = 4 2 x , h ( x ) = 0

To determine

To graph: The region bounded by the graphs of functions f(x)=2x, g(x)=42x and h(x)=0 using a graphing calculator, and to write the definite integral that represents the area of the region.

Explanation

Given Information:

The region bounded by the graphs of f(x)=2x, g(x)=42x and h(x)=0.

Graph:

Consider the following functions,

f(x)=2x, g(x)=42x and h(x)=0

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

Step 1: Press "Y=" key. Insert three functions as Y1=2x, Y2=42x and Y3=0.

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

Xmin=1, Xmax=3,Xscl=1Ymin=0, Ymax=4,Yscl=1

Step 3: Press “2nd”, “Trace” and then “5” key to compute intersection point. Press “Enter” key three times. The intersection point of two graphs is found as (1,2).

Step 4: Press “2nd”, “Mode”, “2nd” 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 “Y3” and press “Enter.” Press “,” key, “Vars”, right arrow key and press “Enter.” Scroll to “Y1” and press “Enter.” Press “,” key, type “0” as lower limit, press “,” key, “2nd” and “” key. Press “)” key and press “Enter.” The screenshot is as follows:

The graph will be shown as follows:

Step 6: Press “2nd”, “Mode”, “2nd” 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 “Y3” and press “Enter.” Press “,” key, “Vars”, right arrow key and press “Enter.” Scroll to “Y2” and press “Enter.” Press “,” key, press “,” key, “2nd” and “” key, type “2” as upper limit. Press “)” key and press “Enter.”

The required region will be shown as follows:

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