Question

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.

Answer 1

are there any points where it is infinity?

Answer 2

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 ln|csc(x)+cot(x)|.
Approaching pi from the left side, I get ln|inf-inf|, 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?