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Math Help - Intergrals Problems

  1. #1
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    Intergrals Problems

    1. Finding indefinite integrals (without the integration constant).
    ????

    How come the answer is not (cosx)(sinx)(x)??
    What does (without the integration constant) mean?
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  2. #2
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    NEvermind, i already solved number 2. Just need help on 1 thanks.
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  3. #3
    MHF Contributor Calculus26's Avatar
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    remember if the integral of f is F then F ' = f

    So differentiate cos(x)sin(x)*x and you won't get sin(x)cos(x)

    Now I think you are thinking "integral of fg = integral of f times integral of g"

    but this isn't correct.
    There is no product rule for integration
    But even for derivatives (fg) ' is not simply f ' g' is it ?

    There are 2 ways to solve your integral

    1, using u substitution let u = sin(x) or u = cos(x) either will work here

    2.use the identity sin(x)cos(x) =1/2sin(2x) and use u = 2x
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