   Chapter 5.5, Problem 10E ### 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. ∫ − 4 0 [ ( x − 6 ) − ( x 2 + 5 x − 6 ) ] d x

To determine

To graph: The function from the integrand 40[(x6)(x2+5x6)]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 40[(x6)(x2+5x6)]dx.

Graph:

Consider the provided integral,

40[(x6)(x2+5x6)]dx

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

f(x)=x6

And g(x)=x2+5x6

Consider the first function f(x)=x6

It is a linear function. So, its graph will be a straight line with slope m=1 and y-intercept b=6

Consider the second function g(x)=x2+5x6

It is a quadratic function. So, its graph will be a parabola with opening upwards. Factor the function,

g(x)=x2+5x6=x2+6xx6=x(x+6)1(x+6)=(x+6)(x1)

The x-intercepts are x=6 and x=1

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