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Recurrence formula

  • Thread starter hechnal
  • Start date
2
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1. Homework Statement
I(subscript n)=integral (from pi/2 to 0) [sin(x)]^n * [cos(x)]^2.

Show that I (subscript n) = [(n-1)/(n+2)] I(subscript (n-2))

I think ur meant to use integration by parts on it somewhere but i don't know wat to use it on.
 

Answers and Replies

HallsofIvy
Science Advisor
Homework Helper
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Since In-2 involves sinn-2[/sub] it seems clear to me that you want to reduce the the power on sinn(x) and you can do that by differentiating (twice). Try an integration by parts (twice) letting u= sinn(x) and dv= cos2(x)dx. (To find v, it might help to remember that cos2(x)= (1/2)(1+ cos(2x))
 

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