can some one help me with this integration problem?>?

Question

I have to find the intergral of cos^2(phata)

I know cos^2(phata) = (1 + cos2(phata))/ 2

I bring out the 1/2 to the other side of the integration sign

1/2 intergral 1 + cos(2phata)

would the answer be 0.5 (phata + sin 2phata)?

I think I have to do something with the 2 phata?

Answer 1

You've almost got it, regarding the 2 inside the bracket, you need to deal with it using the chain rule (by dividing the term by 2).

You're answer should be :
0.5 (phata + (1/2)sin (2phata))

Answer 2

Let x = "phata"
I = ∫ cos ² x dx
Now cos 2x = 2cos ² x - 1
2 cos ² x = 1 + cos 2x
cos ² x = (1/2) + (1/2).cos 2x
I = (1/2).∫ 1 + cos 2x dx
I = (1/2) x + (1/4).sin 2x + C

Answer 3

calling phata = t
Int 1/2(1+cos2t)dt = 1/2(t+sin 2t *1/2) as the derivative of sin2t= 2*cos2t(chain rule)