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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 2

Evaluate the improper integral, if possible.

0 1 ( x 1 ) 2 d x

To determine

To calculate: The value of the improper integral 01(x1)2dx if possible.

Explanation

Given Information:

The expression is provided as:

01(x1)2dx

Formula used:

From definition of improper integral.

bf(x)dx=limaabf(x)dx

Also, the expression for the integration of a inverse function is as follows:

1xdx=|x|+C

Calculation:

Consider the provided integral:

01(x1)2dx

Use the property of improper integral and simplify as:

01(x1)2dx=lima01(x1)2dx

Integrate the integrand by substitution method as:

Assume x1=u

Differentiate as:

dx=du

Now, substitute the values and integrate by using the inverse function formula as:

1(x1)2dx=1u2du=1u+C

Again, substitute the value of u

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