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September 9th, 2017, 05:55 AM   #1
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Integral of sin(x)*cos(x)

Hello

I don't understand why I get different results when I try to find that integral.
If I choose f' as cos(x) and g as sin(x) then using the partial integration formula the result is (1/2)*sin^2(x).
If I choose f' as sin(x) and g as cos(x), then the result is -(1/2)*cos^2(x).

The two results are not equal, so something is wrong (the 2nd result is correct).

Last edited by skipjack; September 9th, 2017 at 01:22 PM.
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September 9th, 2017, 07:06 AM   #2
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Recall that $\sin^2 x + \cos^2 x = 1$ so the two results differ only by an additive constant. Thus they have the same derivative and are therefore both primitives of the same function (your integrand).

Note that an easier way to get a (third different) result is to use $\sin 2x = 2\sin x \cos x$ to simplify the integrand before you integrate.
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September 9th, 2017, 07:45 AM   #3
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oh,I see,thanks
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