Chapter 8.8, Problem 46E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Evaluating an Improper Integral In Exercises 33–48, determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. ∫ 4 ∞ x 2 − 16 x 2   d x

To determine
Whether the improper integral 4x216x2dx converges or diverges.

Explanation

Consider the provided integral,

âˆ«4âˆžx2âˆ’16x2dx=âˆ«4âˆžx2âˆ’42x2dx

Now, use the formula:

âˆ«aâˆžf(x)dx=limcâ†’âˆžâˆ«acf(x)dx

Then,

âˆ«4âˆžx2âˆ’42x2dx=limbâ†’âˆžâˆ«4bx2âˆ’42x2dx

Now, apply the formula:

âˆ«x2âˆ’a2x2dx=âˆ’x2âˆ’a2x+ln|

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Single Variable Calculus: Early Transcendentals, Volume I