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when I integrate $\sin x \cos x$ using $u$ substitution I'm getting $\frac{1}{2}\sin^2 x$ and $-\frac{1}{2}\cos^2 x$, I cannot identify the relationship here

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    $\begingroup$ $\int f(x)dx=F(x) + \color{red}{C}$. The two answers are different by a constant. $\endgroup$ – Quang Hoang Mar 1 '16 at 3:10
  • $\begingroup$ I assume the sign is being affected by the possible values of C, is it right? $\endgroup$ – Christian Andrews Mar 1 '16 at 3:13
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    $\begingroup$ $\frac 1 2 - \frac 1 2\cos^2 x = \frac 1 2\sin^2 x$. $\endgroup$ – Friedrich Philipp Mar 1 '16 at 3:15
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    $\begingroup$ @ChristianAndrews $\sin^2x+\cos^2x=1$ implies $\sin^2x=-\cos^2x+1$, so the switch in sign is not in error (try graphing it if you are unconvinced) $\endgroup$ – Peter Woolfitt Mar 1 '16 at 3:15
  • $\begingroup$ God, now I get it, thanks guys @PeterWoolfitt Friedrich Quang $\endgroup$ – Christian Andrews Mar 1 '16 at 3:21

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