Posted by Sam on Monday, June 4, 2012 at 3:51pm.
Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent).
I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral.

Calculus  bobpursley, Monday, June 4, 2012 at 4:34pm
are there any points where it is infinity?

Calculus  Sam, Tuesday, June 5, 2012 at 12:48am
Thank you for your help, Bob.
I will be more clear regarding exactly where I do not understand.
I know I need to take the limit on the upper bound (e.g. A) as it approaches pi from the left side.
After doing so, I get lncsc(x)+cot(x).
Approaching pi from the left side, I get lninfinf, so I need to do L'Hopital's Rule.
I common denominator, and get ln(1+cos(A))/(sin(A)).
As A approaches pi, I get ln(0), which is still not defined.
Does this mean that the integral diverges?