This one has had me stuck for a good hr.
The integral has a min of 0 and a max of 1.
S (4-x)/(sqrt(4-x^2)) dx
I'm trying to use the formula S (du)/(sqrt(a^2-u^2)) = arcsin u/a + C
I set "u" = (x^2), "du" = 2x, and a = 2.
Typically the problems I get will have the du equal the numerator and it's pretty easy from there. But my du does not equal the numerator and I'm stuck.
I think the answer for the interval (disregarding the min and max) is:
Sqrt(4-x^2) + 4 arcsin(x/2) + C.
And the part in underlined bold I have absolutely no idea where it came from.
And the final answer:
-2 + Sqrt(3) + (2pi)/3
Basically I cannot figure a way to get that answer or the steps involved. Can anyone help? Thank you.