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July 28, 2015

Homework Help: Calculus

Posted by Sam on Tuesday, June 5, 2012 at 12:49am.

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, at the following particular step.

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?

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