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Finding integrand of trig function.

  1. Aug 9, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]\int sin^4({\Pi\theta}) cos^3({\Pi\theta}) d\theta[/tex]


    3. The attempt at a solution
    let x = theta to make things simpler in text
    let u = sin (pi x)
    du = (1/pi) cos (pi x) dx

    integral sin^4(pi x) cos^3(pi x) dx
    = integral sin^4(pi x) cos^2(pi x) cos (pi x) dx
    = integral sin^4(pi x) [1-sin^2 (pi x)] cos (pi x) dx
    = integral sin^4(pi x) cos(pi x) . sin^6(pi x) cos(pi x) dx
    = (1/pi) integral u^4 + u^6 du
    = (1/pi) (u^5/5+u^7/7) + c
    = u^5/5pi + u^7/7pi + c.

    I know the answer is wrong, but I think the method I used was following the textbook. Can someone point out where I was wrong?

    Thank you! :)
     
  2. jcsd
  3. Aug 9, 2009 #2

    VietDao29

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    Homework Helper

    The Multiplication Sign there is incorrect. :(

    Wrong sign. :(

    Apart from those little (and "silly") mistakes, everything looks just fine to me. :)

    Ah, I forgot to mention that you also need to switch u back to x. Since the problem is in terms of x, so it's more natural to have the result displayed in terms of x, too. :)
     
    Last edited: Aug 9, 2009
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