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posted by  FuturePMP on 8/17/2007 10:03:09 PM  |  status: Closed  

Improper integral

Course Textbook Chapter Problem
Calculus Calculus With Analytic Geometry (8th) by Edwards, Larson, Hostetler 8.8 40E
Question Details:

The square is a typo
Determine whether the improper integral diverges or converges, evaluate if it converges.
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posted by Peterson on 8/17/2007 10:40:16 PM  |  status: Live
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FuturePMP's comment:
"Thank you so much the pi/2 explanation helped me on another hand ful of problems"
Response Details:
Because is not defined when , we have


           
The general integral would be


We make the substitution , and we have , and the integral becomes


              
              

Back to our improper integral, we have


as t approaches pi/2 from the negative side


Divergent.

                           
               


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