Can someone plese tell me what is integration of sin(x)cos(x)?

Question

Thanks in advance

Answer 1

Let u = sinx.

Then du = cosx dx.

So it's the same as integrating u...you get:

∫ sinx (cos x dx) = ∫ u du = 1/2 u² + C = 1/2 (sin²x) + C

Answer 2

Ok let it be simple like this
no need to put U as a substitution since its simple in this and can be solved without any substitution
sin2x=2sinxcosx
sin2x/2=sinxcosx
integration of sin2x/2 dx=integration of sin2x/2
answer is (-cos2x/4)+c
now if this is wht u wanted please choose it as the best answer

Answer 3

sin(x)cos(x) = 1/2sin(2x)

integral of 1/2sin2x = -1/4cos(2x)

Note: my answer and Jim's are the same - remember there is an additive constant.

-1/4cos(2x) + C = 1/4(sin^2x - cos^2x) + C
let C = 1/4 = 1/4(cos^2x + sin^2x), then
1/4(sin^2x - cos^2x) + 1/4(cos^2x + sin^2x) = 1/2sin^2x

Answer 4

2sin(x)cos(x) = sin(2x)
sin(x)cos(x) = 0.5sin(2x)
Integrate sin(x)cos(x) = -2(0.5)cos(x) + c
= -cos(x) + c, where c is an arbitary constant

Answer 5

1/2 sin^2(x)..............i really dont''t know how to explain, but this is the answer