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.
2 answers
are there any points where it is infinity?
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?
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?
2 answers