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Math Help - how do you do this integral

  1. #1
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    how do you do this integral

    sin(wt)cos(nwt) dt
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  2. #2
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    Quote Originally Posted by richard7893 View Post
    sin(wt)cos(nwt) dt
    u=\cos(nwt)

    Make this integral into the form of udu and it integrates easily.
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  3. #3
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    But if you do this your du=-nwsin(nwt). By doing this you cant substitute for sin(wt) because du=-nwsin(nwt)
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  4. #4
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    Quote Originally Posted by richard7893 View Post
    But if you do this your du=-nwsin(nwt). By doing this you cant substitute for sin(wt) because du=-nwsin(nwt)
    Ooops! Sorry I missed that. Eyes are wearing out from looking at the computer.

    Hmmm, my first thought is to try the product to sum conversation for sin(a)cos(b), which looks like:

    \sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}

    That should split up into things you can integrate separately easily.
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