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Homework Help: Integration using substitution

  1. Dec 7, 2007 #1
    [SOLVED] Integration using substitution

    Problem: Find the integral of:
    [tex]\int\sin^{6}\theta\cos\theta d\theta[/tex]

    My attempt:

    Let [tex]u\equiv\cos\theta[/tex]
    so: [tex]du\equiv\sin\thetad\theta[/tex]

    Only I don't know where to go from there.

    The book says it should [tex]\frac{1}{7}\sin^{7}\theta+C[/tex] but I have no idea how they got that.

    I'm probably missing something obvious here.
    Last edited: Dec 7, 2007
  2. jcsd
  3. Dec 7, 2007 #2


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    Gold Member

    Try letting [tex]u=sin \theta [/tex]
  4. Dec 7, 2007 #3


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    Your are much better off letting u=sin(x).
  5. Dec 7, 2007 #4
    Ah, that was the totally obvious thing I was missing. For some reason, I decided that the derivative of Sin(x) was...Sin(x)...

    Thanks guys.
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