Chapter 6, Problem 16TYS

### 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
1 views

# In Exercises 14–17, determine whether the improper integral diverges or converges. Evaluate the integral if it converges. ∫ − ∞ 0 1 ( 4 x − 1 ) 2 / 3 d x

To determine

Whether the improper integral 01(4x1)23dx diverges or converges and evaluate if it converges.

Explanation

Consider the provided integral:

01(4x1)23dx

From the definition of improper integral.

af(x)dx=limbabf(x)dx

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

xndx=xn+1n+1+C

Here, n0.

Use the property of improper integral and simplify as:

01(4x1)23dx=limbb01(4x1)23dx

Use the formula for polynomial to integrate the above integral

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