Infinite intervals of integration Evaluate the following

Chapter 7, Problem 5E

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QUESTION:

Infinite intervals of integration  Evaluate the following integrals or state that they diverge.

\(\int_{1}^{\infty} x^{-2} d x\)

Questions & Answers

QUESTION:

Infinite intervals of integration  Evaluate the following integrals or state that they diverge.

\(\int_{1}^{\infty} x^{-2} d x\)

ANSWER:

Problem 5E

Infinite intervals of integration Evaluate the following integrals or state that they diverge.

Solution

Step 1

In this problem we have to evaluate   and then we have to state whether it diverges or not.

Consider  

By using  we get

        

Substituting the limits we get,

        

Now considering  we get

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