   Chapter 5.5, Problem 9E ### 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. ∫ 0 4 [ ( x + 1 ) − 1 2 x ] d x

To determine

To graph: The function from the integrand 04[(x+1)12x]dx and shade the region that will covered by the provided integrand.

Explanation

Given Information:

The provided integrand is 04[(x+1)12x]dx.

Graph:

Consider the provided integrand is,

04[(x+1)12x]dx.

From the above integrand, let the f(x)=x+1 and g(x)=12x and the limit for the area of the integrand is x=0 and x=4.

Now, draw the graph of the function f(x)=x+1 by point plotting method.

Substitute 0 for x in the function f(x)=x+1.

f(0)=0+1=1

Substitute 1 for x in the function f(x)=x+1.

f(1)=1+1=2

Substitute 1 for x in the function f(x)=x+1.

f(1)=1+1=0

Substitute 2 for x in the function f(x)=x+1.

f(2)=2+1=1

Now, make the table for the corresponding value of x and y for the function f(x)=x+1 is shown below,

 x f(x)=x+1 0 1 1 2 −1 0 −2 −1

Now, draw the graph of the function g(x)=12x by point plotting method

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