Question

integral of cos (x/2)

Answer 1

@mathmale

Answer 2

Hello, DS!
What is the integral of plain cos x? Bet you know that.

Answer 3

sin x

Answer 4

my mind's blank right now...

Answer 5

I know the feeling! :)

The integral of cos x is indeed sin x (plus C).

Now, back to your post. What is the integral of cos (x/2)?

Answer 6

You might want to try using the substitution u=x/2.

Answer 7

no clue...
is it sin x/2 ?

Answer 8

Almost. Let u=x/2. Then (du/dx)=dx/2. Can you agree with that?

Answer 9

sin x^2 /4

Answer 10

In the long run it'd be more productive to show all your work. That way I can give you more meaningful feedback than "right" or "wrong."

If we let u=x/2, then du/dx = 1/2, so that du = dx/2, or 2du = dx.

Then your integral of cos x/2 with respect to x becomes \[\int\limits_{}^{}\cos u (2du)\rightarrow 2\int\limits_{}^{}\cos u du=??\]

Answer 11

cos x/4

Answer 12

\[\int\limits\limits_{}^{}\cos u (2du)\rightarrow 2\int\limits\limits_{}^{}\cos u du=2 \sin u + C\] Please make sure you're comfortable with this before we proceed further.

Answer 13

i meant