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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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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 ) = 3 2 x x 2 , g ( x ) = 0

To determine

To graph: The region bounded by the graphs of functions f(x)=32xx2 and g(x)=0 using a graphing calculator, and find the area of the region.

Explanation

Given Information:

The region bounded by the graphs of f(x)=32xx2 and g(x)=0.

Graph:

Consider the following functions,

f(x)=32xx2 and g(x)=0

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

Step 1: Press "Y=" key. Insert two functions as Y1=32XX^2 and Y2=0.

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

Xmin=4, Xmax=2,XScl=2 Ymin=2, Ymax=4,YScl=2

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 (3,0).

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 (1,0).

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 “Y2” and press “Enter.” Press “,” key, “Vars”, right arrow key and press “Enter.” Scroll to “Y1” and press “Enter.” Press “,” key, type “3” as lower limit, press “,” key, and type “1” as upper limit. Press “)” key and press “Enter.”

The graph 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 [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:

From the above, the required area is bounded by the graphs of f(x)=32xx2, g(x)=0, x=3 and x=1

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