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Math Help - How to calculate this

  1. #1
    Junior Member
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    Question How to calculate this

    Okay, so I have this reduction formulae question
    Establish a reduction formula to find Im,n =∫cos m x . sin n x dx
    Prove that (m+n). Im,n = (m-1) . Im-2,n

    And okay I solve the problem above, but then the question says
    evaluate I5,6

    and I can't find the value 8/693 which is the answer in answer key. I'm so confused, what I need to do is just substituting the value right?
    But the problem is the I is the integral of ∫cos m x . sin n x dx so what to do with x, do we just put whatever on x, or what?

    Please help me ! thanks
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  2. #2
    Super Member
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    Re: How to calculate this

    You forgot to mention the limits of integration, which I think are 0 to \pi/2.

    You use the reduction formula twice to get I_{5,6} = some number times I_{1,6}. Then I_{1,6}=\int_0^{\pi/2}\cos{x}\sin^6{x}\,dx can be integrated by substituting u=\sin{x}.

    - Hollywood
    Thanks from Deci
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  3. #3
    Junior Member
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    Re: How to calculate this

    Thanks for your help . I understand this now
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