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Math Help - Trigonometric Integration Question

  1. #1
    Super Member craig's Avatar
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    Trigonometric Integration Question

    Hi, just a quick question.

    Doing a bit of Fourier Series and I've come across this integral, is there a best way to go about doing this?

    \frac{2}{\pi} \int_0^{\pi} \cos{(x)} \sin{(nx)} dx, where n is an integer 0 \leq n \leq \infty.

    I've attempted by using the product to sum formulas, but this just ends up with at least two sides of tricky algebra.

    Has anyone come across this before, or have any helpful 'shortcuts'?

    Thanks in advance for your help
    Last edited by craig; January 20th 2011 at 07:47 AM.
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    What do you mean with trick algebra?
    It is easy.
    All what you need is : sin(A)cos(B)=\dfrac{1}{2} \left( sin(A-B) + sin(A+B) \right)
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  3. #3
    Super Member craig's Avatar
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    Quote Originally Posted by Liverpool View Post
    What do you mean with trick algebra?
    It is easy.
    All what you need is : sin(A)cos(B)=\dfrac{1}{2} \left( sin(A-B) + sin(A+B) \right)
    Ohh sorry, meant tricky algebra.

    I've sort of done it with the product to sum formulas, was just wondering if anyone know of a shorter way.
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  4. #4
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    Quote Originally Posted by craig View Post
    Ohh sorry, meant tricky algebra.

    I've sort of done it with the product to sum formulas, was just wondering if anyone know of a shorter way.
    That IS the shortest way...
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  5. #5
    Super Member craig's Avatar
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    Ahh thought as much, merci
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