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Integral of sin^2t*cos^4t

  1. Jan 27, 2012 #1
    1. The problem statement, all variables and given/known data

    [itex]\int^{0}_{pi}(sin^{2}t)*(cos^{4}t)[/itex]

    2. Relevant equations



    3. The attempt at a solution

    I know you have to use trig identities.. but everything I try does not work.
     
  2. jcsd
  3. Jan 27, 2012 #2
    The limits of the integral should be reversed.
     
  4. Jan 27, 2012 #3

    Dick

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    You can do it with double angle identities. But you haven't shown anything you've tried yet. What did it occur to you to try?
     
  5. Jan 27, 2012 #4

    SammyS

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    [itex]2\sin(\theta)\cos(\theta)=\sin(2\theta)[/itex]

    So, sin2(θ)cos2(θ) =   ?  

    [itex]2\cos^2(\theta)-1=\cos(2\theta)[/itex]

    So, cos2(θ) =   ?  
     
  6. Jan 27, 2012 #5
    cos^2(t)=1-sin^2(t), then you use the double cos identity until you reduce it down to combination of cos(2t)'s,
     
    Last edited: Jan 27, 2012
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