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Homework Help: Trig integral

  1. Nov 3, 2007 #1
    1. The problem statement, all variables and given/known data
    I'm actually in the middle of a multivariable question, and I am stuck because I don't remember how to integrate [tex]sin(\phi)cos(\phi)[/tex] .


    3. The attempt at a solution
    I have an understanding of the material, but I can't remember how to integrate this. Someone please refresh my memory :) . I would appreciate some kind of step by step integration, so if this was on the test I would understand how to do it.
     
  2. jcsd
  3. Nov 3, 2007 #2
    What is the derivative of sin? Do you remember substitutions?
     
  4. Nov 3, 2007 #3
    The derivative of sin(x) is cos(x), and I do remember substitutions, but I dont know what to substitute, because I can't remember any identities for sin or cos with a power of 1.
     
  5. Nov 3, 2007 #4
    Do you remember substituting for U then finding the dU, which is the derivative of the U, then making substitutions to the original integral to change the integral interms of the variable U? Make U=sin(x), then what is dU?
     
  6. Nov 3, 2007 #5
    That is so weird. I didnt even think about that. Can you explain why that works, but the integral of sin(x) by itself is -cos(x)? (if your answer is 'it just is' that is perfectly fine). I thought of u substitution--I was thinking that it wouldn't work.
     
  7. Nov 3, 2007 #6
    maybe this will make it easier

    [tex]sin{2x}=2sin{x}cos{x}[/tex]

    [tex]\int\sin{x}cos{x}dx[/tex]

    so

    [tex]\frac{1}{2}\int\sin{2x}dx[/tex]
     
  8. Nov 3, 2007 #7
    messed up with my latex, still trying to get the hang of it.
     
    Last edited: Nov 3, 2007
  9. Nov 3, 2007 #8
    Let U=sinx

    then, dU=cosxdx

    so if you substitute thes identities to the original equation:
    [tex]\int[/tex]UdU

    Can you integrate that? Then sub it back in with the same identities after you integrate
     
  10. Nov 3, 2007 #9

    cristo

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    I think rocophysic's method is simpler, since it does not involve any substitutions.
     
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