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Posted by 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 - , Monday, June 4, 2012 at 4:34pm

    are there any points where it is infinity?

  • Calculus - , 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 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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