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## Resolved Question

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# How do I integrate Cos x Sin x dx?

How do I integrate Cos x Sin x dx? I'm working on an engineering problem and having trouble getting up to speed with simple integral calculus. Any help is much appreciated!
Member since:
September 23, 2006
Total points:
11,913 (Level 6)

you can solve in different ways you will get diff answer but they will be right

1) put sinx = t
cosxdx = dt

∫ tdt = t^2/2 +c = 1/2sin^2 X +c

2) sinxcosx = 1/2 sin2x
∫ 1/2sin2x dx = -1/4 cos2x +c
• 2 people rated this as good
Great answer --- thanks! The others were great, too, but this answer listed two approaches.
This answer has got the substitution the wrong way round.

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• by yucd
Member since:
May 13, 2007
Total points:
149 (Level 1)
cosx sinx dx = 1/2sin^2 x +c ,meaning half of sinx square
also cosxsinx = -1/2cos^2 x + c ,means half of cos square negative.
• Member since:
August 26, 2008
Total points:
498 (Level 2)
cos(x)*sin(x)=1/2 *sin(2x)=>
int(cosx*sinx*dx)=int(1/2*sin(2x)dx)
=-1/4*cos(2x)
• 1 person rated this as good
• by sahsjing
Member since:
December 19, 2006
Total points:
230,933 (Level 7)
∫cosx sinx dx
= ∫sinx dsinx
= (1/2)sin^2(x) + c