   Chapter 7.8, Problem 54E

Chapter
Section
Textbook Problem

# Use the Comparison Theorem to determine whether the integral is convergent or divergent. ∫ 0 π sin 2 x x   d x

To determine

whether the given integral is convergent or divergent, by using the comparison theorem.

Explanation

Given:

0πsin2xxdx.

Formulae used:

xndx=1n+1xn+1+c.

Since 0<sin2x1 for all x,x(0,π)

Therefore, sin2xx1x

Now

0π1xdx=limt0+

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