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Math Help - Integral Proofs

  1. #1
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    Integral Proofs

    Prove the formula, where m and n are positive integers

    a) Integral(-pi to pi) sin(mx) cos(nx)dx = 0.


    b) Integral(-pi to pi) sin(mx)sin(nx)dx = 0 if m != n

    Integral(-pi to pi) sin(mx)sin(nx)dx = pi if m = n


    c) Integral(-pi to pi) cos(mx) cos(nx) dx = 0 if m != n

    Integral(-pi to pi) cos(mx) cos(nx) dx = pi if m = n

    I don't even know where to start with this problem!!! /
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  2. #2
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    Quote Originally Posted by TreeMoney View Post
    Prove the formula, where m and n are positive integers

    a) Integral(-pi to pi) sin(mx) cos(nx)dx = 0.


    b) Integral(-pi to pi) sin(mx)sin(nx)dx = 0 if m != n

    Integral(-pi to pi) sin(mx)sin(nx)dx = pi if m = n


    c) Integral(-pi to pi) cos(mx) cos(nx) dx = 0 if m != n

    Integral(-pi to pi) cos(mx) cos(nx) dx = pi if m = n

    I don't even know where to start with this problem!!! /
    I give you a killer hint.
    Use identities

    sin x sin y= (1/2)[cos(x-y)-cos(x+y)]

    cos x cos y=(1/2)[cos(x-y)+cos(x+y)]

    sin x cos y=(1/2)[sin(x+y)+sin(x-y)]

    Just curious are you learning Fourier Series?
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  3. #3
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    no, this is all different ways of integration. But my issue is I don't remember any trig whats so ever, So I'm trying to learn new material and re-teach basically teach myself all of trig over again. I think the last time I did anything using this much trig was like 6 or 7 years ago.
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  4. #4
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    Quote Originally Posted by TreeMoney View Post
    no, this is all different ways of integration. But my issue is I don't remember any trig whats so ever, So I'm trying to learn new material and re-teach basically teach myself all of trig over again. I think the last time I did anything using this much trig was like 6 or 7 years ago.
    The important thing is to understand how these formulas are true. Then you do not need to memorize them. For example, when you asked this question I did not have to look them up nor memorize these identities. I just know that cos(x+y) leaves cosine with cosine and sine with sine and the rest was trivial. I was just reading CaptainBlank said he does not know the quotient rule but still solved the problem because he understands how it works.
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