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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Checkpoint 1 Worked-out solution available at LarsonAppliedCalculus.com

Find the area of the region bounded by the graphs of

y   =   x 2 +   1  and  y = x   f o r   0   x   2 .

Sketch the region bounded by the graphs.

To determine

To calculate: The area bounded by graph of the function y=x2+1 and y=x from the limit 0x2 and also sketch the bounded region by graph of the function.

Explanation

Given Information:

The provided function is y=x2+1 and y=x and the limit is 0x2.

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=x2+1.

Now, draw the graph by using point plotting method.

Substitute 0 for x in the function y=x2+1.

y=02+1=1

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

y=12+1=2

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

y=(1)2+1=2

Substitute 2 for x in the function y=x2+1.

y=(2)2+1=4+1=5

Now, make the table for the corresponding value of x and y for the function y=x2+1 is shown below,

x y=x2+1
0 1
1 2
1 2
2 5

Consider the function y=x.

Now, draw the graph by using point plotting method.

Substitute 0 for x in the function y=x.

y=0

Substitute 1 for x in the function y=x

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