   Chapter 7.8, Problem 40E

Chapter
Section
Textbook Problem

# Determine whether each integral is convergent or divergent. Evaluate those that are convergent. ∫ 0 1 e − 1 / x x 3   d x

To determine

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

Explanation

Given:

01e1xx3dx

Formula used:

ddx(xn)=nxn1f(x)g(x)dx=f(x)g(x)dx[f(x)g(x)dx]dxexdx=ex+c.

Let I=01e1xx3dx

Assume that:

1x=t1x2dx=dt

When,

x=0   ; t=x=1 ; t=1

And x=1t

Therefore,

=1et(dt)1t=

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