   Chapter 6, Problem 58RE ### 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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# Area of a Region In Exercises 57–60, find the area of the unbounded shaded region. y = 2 x x 2 + 2 To determine

To calculate: The area under the shaded region under the graph of the function y=2xx2+2. Explanation

Given Information:

The equation, y=2xx2+2

And the graph is,

Formula used:

From definition of improper integral.

If on the interval [a,), the function is continuous, then

af(x)dx=limbabf(x)dx

The integral formula:

1xdx=|x|+C

Calculation:

Consider the provided equation:

02xx2+2dx

And the graph,

Use the definition of improper integral af(x)dx=limbabf(x)dx

And simplify as

02xx2+2dx=limb02xx2+2dx

In the provided integral,

Assume x2+2=u

Now, differentiate

2xx2

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