   Chapter 5.5, Problem 2CP ### 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
1 views

# Checkpoint 2 Worked-out solution available at LarsonAppliedCalculus.comFind the area of the region bounded by the graphs of y   = 3   —   x 2  and  y   =   2 x .

To determine

To calculate: The area bounded by graph of the function y=3x2 and y=2x.

Explanation

Given Information:

The provided function is y=3x2 and y=2x.

Formula used:

The function f(x) and g(x) are the continuous function on interval [a,b] and g(x)f(x) for all x in [a,b], then, the area bounded by the graphs of f(x) and g(x),x=a and x=b is,

A=ab[f(x)g(x)]dx

Calculation:

Consider the function y=3x2.

Now, draw the graph by using point plotting method.

Substitute 0 for x in the function y=3x2.

y=302=3

Substitute 1 for x in the function y=3x2.

y=312=2

Substitute 1 for x in the function y=3x2.

y=3(1)2=2

Substitute 2 for x in the function y=3x2.

y=3(2)2=1

Now, make the table for the corresponding value of x and y for the function y=3x2 is shown below,

 x y=3−x2 0 3 1 2 −1 2 −2 −1

Consider the function y=2x.

Now, draw the graph by using point plotting method.

Substitute 0 for x in the function y=2x.

y=20=0

Substitute 1 for x in the function y=2x.

y=21=2

Substitute 1 for x in the function y=2x.

y=2(1)=2

Substitute 2 for x in the function y=2x.

y=2(2)=4

Now, make the table for the corresponding value of x and y for the function y=2x is shown below,

 x y=2x 0 0 1 2 −1 −2 −2 −4

Draw the graph of the function y=3x2 and y=2x by using above table

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