Chapter 8.8, Problem 10E

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

# Evaluating an Improper Integral In Exercises 13-16, explain why the integral is improper and determine whether it diverges or converges. Evaluate the integral if it converges. ∫ 3 4 1 ( x − 3 ) 3 / 2 d x

To determine

If the integral 341(x3)3/2dx is improper, will the integral converge and determine the value of the integral. The graph of the integral is shown below

Explanation

Given:

The provideddiagram for the integral is 341(x3)3/2dx is

Explanation:

To check if the function is improper, and determine the point of infinite discontinuity

For this consider 1(x3)3/2= and find x:

1(x3)3/2=(x3)3/2=0x3=0x=3.

The point of discontinuity lies between upper limit and lower limit.

∴, it is concluded that given function is not continuous on interval [3,4].

Hence, given integral is improper.

Now, known fact is that, an improper integral converges when the limit of the integral exists.

341(x3)3/2=limb3+b41(x3)3/2

Integrate 1(x

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