Thread: indefinite integral

int {pi/4}^{pi/2} \ csc^{2}x dx

im so lost when trying to do this problem. i know that csc is 1/sin.
i've tried using the half-angle identity but it didnt work.
can someone explain.

Originally Posted by viet

int {pi/4}^{pi/2} \ csc^{2}x dx

im so lost when trying to do this problem. i know that csc is 1/sin.
i've tried using the half-angle identity but it didnt work.
can someone explain.

You are making it too complicated.

First, INT sec^2 x dx = tan x+C
That is a well known integral.

Similarly, INT csc^2 x dx = -cot x+C
(Just note the negative, because like with sine and cosine the signs change when you look at them).

so now do i evaluate pi/4 to pi/2 for -cot(x)?

Originally Posted by viet

so now do i evaluate pi/4 to pi/2 for -cot(x)?

Yes. Integral evaluted at upper limit minus the lower limit.