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Math Help - Why are these two integrals not equal to each other?

  1. #1
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    Why are these two integrals not equal to each other?

    Hi

    I have this integral:

    integrate (sin(ax)cos(ax))

    I used the identity that sinxcosx = 0.5sin(2x)

    yet when I integrate (0.5sin(2ax)) it doesnt come out as the same answer as the original integral - at least not according to wolfram alpha's equality check-
    Can anyone explain this?

    Thanks

    EDIT - a is just a constant
    Last edited by willsor; March 4th 2013 at 11:39 AM.
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  2. #2
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    Re: Why are these two integrals not equal to each other?

    Quote Originally Posted by willsor View Post
    integrate (sin(ax)cos(ax))
    I used the identity that sinxcosx = 0.5sin(2x)
    yet when I integrate (0.5sin(2ax)) it doesnt come out as the same answer as the original integral - at least not according to wolfram alpha's equality check-
    You may try any of these. They all work.

    \frac{\sin^2(ax)}{2a},~-\frac{\cos^2(ax)}{2a},~\frac{-\cos(2ax)}{4a}~
    Thanks from willsor
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  3. #3
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    Re: Why are these two integrals not equal to each other?

    Ok great - why can I not use this identity to make it easier in this case?
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  4. #4
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    Re: Why are these two integrals not equal to each other?

    derp, I just realised.. Thanks for the help
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  5. #5
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    Re: Why are these two integrals not equal to each other?

    When you integrate two equal expressions, you might get two different results, but they all have to vary by a constant. An example would be cos(x)^2 and -sin(x)^2. Don't forget to account for the constant of integration.
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