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Math Help - trig integral

  1. #1
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    Question trig integral

    I tried to solve this integral but i was not able to get an answer. I tried foiling the integrand and go from there but was not able to succeed.

    Find integral

    integral from 0 to pi (xsinx+cosx)(xcosx+sinx)dx


    THey gave me a hint
    Hint: sinxcosx= 1/2sin2x

    So far i just foiled and got the following for the integrand:

    x^2sinxcosx + xsin^2x+ xcos^2x + cosxsinx dx
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  2. #2
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    Quote Originally Posted by swimmergirl View Post
    I tried to solve this integral but i was not able to get an answer. I tried foiling the integrand and go from there but was not able to succeed.

    Find integral

    integral from 0 to pi (xsinx+cosx)(xcosx+sinx)dx


    THey gave me a hint
    Hint: sinxcosx= 1/2sin2x

    So far i just foiled and got the following for the integrand:

    x^2sinxcosx + xsin^2x+ xcos^2x + cosxsinx dx
    Remember that \sin^2{x} + \cos^2{x} = 1.

    So x\sin^2{x} + x\cos^2{x} = x(\sin^2{x} + \cos^2{x}) = x(1) = x.

    Also \sin{x}\cos{x} = \frac{1}{2}\sin{2x}.

    Thus the integrand is

    x^2\sin{2x} + x + \frac{1}{2}\sin{2x}.

    This is easier to integrate. You integrate the x^2\sin{2x} using Integration by Parts.
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  3. #3
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    oh ok it makes so much sense. Now, when I substitute 1/2 sin2x into x^2sinxcosx I don't get x^2sin2x...I get x^2 times 1/2 sin2x
    what is wrong with it? i cant see my mistake



    ok i think i got it. I took out the constant 1/2 and then integration by parts for x^2sin2x
    Last edited by swimmergirl; March 18th 2009 at 09:24 PM.
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