Chapter 6.4, Problem 12E

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Evaluating an Improper Integral In Exercises 7-20, determine whether the improper integral diverges or converges. Evaluate the integral if it converges. See Examples 1, 2, and 3. ∫ 5 ∞ 1 x 2 − 16   d x

To determine

Whether the improper integral 5xx216dx diverges or converges and to evaluate the integral if it converges.

Explanation

Given Information:

The expression is provided as:

5xx216dx

From the definition of improper integral.

af(x)dx=limbabf(x)dx

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

xndx=xn+1n+1+C; where n0.

The improper integral converges if the limit exists otherwise the improper integral diverges.

Consider the provided expression:

5xx216dx

Use the property of improper integral and simplify as:

5xx216dx=limb5bxx216dx

Integrate the integrand by substitution method as:

Assume x216=u

Differentiate as:

xx216dx

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