   Chapter 7.8, Problem 39E

Chapter
Section
Textbook Problem

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

To determine

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

Explanation

Given:

10e1xx3dx

Formula used:

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

Let I=10e1xx3dx

Assume that:

1x=t1x2dx=dt

When,

x=0  ; t=x=1; t=1

And x=1t

Therefore,

I=1et(dt)1t=1tetdt

It is known that:

f(x)g(x)dx=f(x)g(x)dx[f(x)g(x)

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