Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

Calculus

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

Convergence or Divergence In Exercises 53–62, use the results of Exercises 49–52 to determine whether the improper integral converges or diverges. ∫ 2 ∞ 1 3 x ( x − 1 )   d x

To determine

To calculate: Whether the improper integral 21x(x1)3dx converges or diverges.

Explanation

Given:

The integral is 21x(x1)3dx.

Formula used:

If p>1, then the integral 11xpdx converges, and diverges if p1.

Comparison test: Suppose the function f and g are continuous and 0g(x)f(x) on the interval [a,]. And, if ag(x)dx diverges. Then, the integral af(x)dx also diverges.

Calculation:

Consider the integral 21x(x1)3dx.

Let f(x)=1x(x1)3 and g(x)=1x23

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