   Chapter 5.5, Problem 40E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding Area In Exercises 35-40, use a graphing utility to graph the region bounded by the graphs of the functions. Find the area of the region by hand. f ( x ) = x 3 − 2 x 2 ; g ( x ) = x 2 − 2 x

To determine

To calculate: The region bounded by the graphs of functions f(x)=x32x2 and g(x)=x22x using a graphing calculator, and also find the area of the region.

Explanation

Given Information:

The region bounded by the graphs of f(x)=x32x2 and g(x)=x22x.

Formula used:

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

If f and g are continuous on [a,b] and g(x)f(x) for all x in [a,b], then the area of the region bounded by the graphs of f, g, x=a and x=b is given by

A=ab[f(x)g(x)]dx

Calculation:

Consider the following functions,

f(x)=x32x2 and g(x)=x22x

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

Step 1: Press "Y=" key. Insert three functions as Y1=x32x2 and Y2=x22x.

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

Xmin=3, Xmax=3, Xscl=1Ymin=3, Ymax=3,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 (0,0).

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

Press “2nd”, “Trace” and then “5” key to compute intersection point. Press “Enter” key two times. Scroll near to third intersection point. The third intersection point of two graphs is found as (2,0).

Step 5: Press “Vars” key, scroll to right and press “Enter” key to open “Functions.” Scroll to “Y2” 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, and type “1” as the upper limit. 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 “Y1” and press “Enter.” Press “,” key, “Vars”, right arrow key and press “Enter.” Scroll to “Y2” and press “Enter.” Press “,” key, type “1” as lower limit, press “,” key and type “2” as upper limit. Press “)” key and press “Enter.” The screenshot is as follows:

The graph will be shown as follows:

Interpretation:

From the above, the required area consists of two regions. First region is the area bounded by the graphs of f(x)=x32x2, g(x)=x22x, x=0 and x=1 with f(x)g(x)

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