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Math Help - indefinite integral

  1. #1
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    indefinite integral

    int {pi/4}^{pi/2} \ csc^{2}x dx

    im so lost when trying to do this problem. i know that csc is 1/sin.
    i've tried using the half-angle identity but it didnt work.
    can someone explain.
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  2. #2
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    Quote Originally Posted by viet View Post
    int {pi/4}^{pi/2} \ csc^{2}x dx

    im so lost when trying to do this problem. i know that csc is 1/sin.
    i've tried using the half-angle identity but it didnt work.
    can someone explain.
    You are making it too complicated.

    First, INT sec^2 x dx = tan x+C
    That is a well known integral.

    Similarly, INT csc^2 x dx = -cot x+C
    (Just note the negative, because like with sine and cosine the signs change when you look at them).
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  3. #3
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    so now do i evaluate pi/4 to pi/2 for -cot(x)?
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  4. #4
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    Quote Originally Posted by viet View Post
    so now do i evaluate pi/4 to pi/2 for -cot(x)?
    Yes. Integral evaluted at upper limit minus the lower limit.
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