   Chapter 5.5, Problem 12E ### 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 the Region In Exercises 9-12, the integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. ∫ − 2 0 [ ( 1 3 x 3 − x ) − 1 3 x ] d x

To determine

To graph: The function from the integrand 20[(13x3x)13x]dx and shade the region that will covered by the provided integrand.

Explanation

Given Information:

The area between the graphs of two functions is represented by the integral 20[(13x3x)13x]dx.

Graph:

Consider the provided integral,

20[(13x3x)13x]dx

Compare it with the formula for the area between two graphs A=ab[f(x)g(x)]dx,

f(x)=13x3x

And g(x)=13x

Consider the first function f(x)=13x3x

It is a polynomial function. Factor the function,

f(x)=13x3x=x(13x21)=x3(x23)=x3(x+3)(x3)

The x-intercepts are x=3,0 and3

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