Question

Can someone help me solve this integral? I have the answer, but I need to understand how to get it. The problem is simple, (integral) of cos^-1 x dx

Answer 1

So, the integral of the inverse cosine function?

Did you have any ideas on how you might begin? The style of the answer might hint at it as well.

Answer 2

Honestly I really need help from the start, I was sick and missed class and just got the answer basically from notes,

Answer 3

Does integration by parts sound familiar?
Or this form:
\( \displaystyle \int u \ dv = uv - \int v \ du \)

Answer 4

can i show u what i have?

Answer 5

Sure. :)

Answer 6

I = ∫cos^-1(x)dx

u = cos^-1(x), then du = -1/sqrt(1-x^2)
dv = dx, then v = x
I = xcos^-1(x) + ∫x/sqrt(1-x^2)dx

u = 1-x^2, then du = -2xdx, and xdx = -1/2du

I = xcos^-1(x) -1/2 ∫du/sqrt(u)

I = xcos^-1(x) -sqrt(u) + c

I = xcos^-1(x) -sqrt(1-x^2) + c

Is this the proper steps?

Answer 7

Yup, that looks right to me.

Answer 8

Ok cool thanks lol wasn't sure

Answer 9

Yeah, no problem! :p