   Chapter 7.8, Problem 14E

Chapter
Section
Textbook Problem

# Determine whether each integral is convergent or divergent. Evaluate those that are convergent. ∫ 1 ∞ e − 1 / x x 2 d x

To determine

whether the given integral is convergent or divergent, evaluate it if convergent.

Explanation

Given:

1e1xx2dx.

Formulae used:

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

1e1xx2dx

This is an improper integral. So we shall use t in place of the limit and take limit t.

So,

1e1xx2dx=limt1te1xx2dx=limx1tx2ex1dx (I)

Taking only integral part of equation

1tx2ex1dx

Let x1=a

So, differentiating with respect to x on both the sides.

So x2dx=da

Thus substituting using a we have

As the limit are not changed for a so again substitute value of a and then take limit

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