   Chapter 13.3, Problem 34E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Use a graphing calculator to find the area between the curves f ( x ) = x 3  and  g ( x )= x 3 − x .

To determine

To calculate: The area of the region enclosed by f(x)=x3, g(x)=x3x.

Explanation

Given information:

The provided curve is:

f(x)=x3, g(x)=x3x

Calculation:

Consider the provided equation:

f(x)=x3, g(x)=x3x

First calculate the intersection points,

The intersection points can be calculated by using Ti-83 calculator and the steps are as follows:

Step 1: Press “ON” key.

Step 2: Press “Y=” key.

Step 3: Enter X^1/3 in front of Y1 and X^3X in front of Y2.

Step 4: Press 2nd key followed by trace key and press “5”.

Step 5: Move the cursor over the first curve and press “ENTER” and then move the cursor over the second curve and press “ENTER”.

Step 6: Press “ENTER” key.

The result is illustrated below:

Thus, the intersection point is (1.34767,1.104873), (0,0) and (1.3487,1.1048).

Thus, the interval is [1.348,1.348].

The steps for calculating the area bounded by the equations f(x)=x3, g(x)=x3x by using Ti-83 calculator are:

The above integral can be solved by using Ti-83 calculator and the steps are as follows

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