How do I integrate Cos x Sin x dx?

Question

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!

Answer 1

Best Answer - Chosen by Asker

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

Asker's Rating:

Asker's Comment:

Great answer --- thanks! The others were great, too, but this answer listed two approaches.

Answer 2

cos(x)*sin(x)=1/2 *sin(2x)=>
int(cosx*sinx*dx)=int(1/2*sin(2x)dx)
=-1/4*cos(2x)

Answer 3

∫cosx sinx dx
= ∫sinx dsinx
= (1/2)sin^2(x) + c

Answer 4

since
dy/dx (cos x) = - sin x

dy/dx (sin x) = cos x

then integrating them wld be the opp of it.

integral of Cos x = sin x

Integral of Sin x = - cos x



Integral of Cos x Sin x
= Integral of Cos x + integral of Sin x
= Sin x - cos x

Answer 5

CosXSinS is as simplified as it gets.