   Chapter 6.4, Problem 8E ### 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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# 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. ∫ 1 ∞ 1 x 3   d x

To determine

Whether the improper integral 11x3dx diverges or converges and to evaluate the integral if it converges.

Explanation

Given Information:

The expression is provided as, 11x3dx

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, 11x3dx

Use the property of improper integral and simplify as:

1

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