   Chapter 5.5, Problem 11E ### 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 2 [ 2 x 2 − ( x 4 − 2 x 2 ) ] d x

To determine

To graph: The function from the integrand 22[2x2(x42x2)]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 22[2x2(x42x2)]dx.

Graph:

Consider the provided integral,

22[2x2(x42x2)]dx

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

f(x)=2x2

And g(x)=x42x2

Consider the first function f(x)=2x2

It is a quadratic function. So, its graph will be a parabola with opening upwards. The graph passes through origin and increases in both directions.

Consider the second function g(x)=x42x2

Factor the function,

g(x)=x42x2=x2(x22)=x2(x2)(x+2)

The x-intercepts are x=2,0 and 2

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