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Math Help - math error on definate integral

  1. #1
    Newbie
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    math error on definate integral

    Hello,

    Im ok with Integration by inspection but cant get this example, see what you think…

    ∫ cot^2 (2x) dx with limits (π/4) and (π/8)

    This is what I get

    (-1/2 cot (2x) – x) with limits
    (-1/2 (1/tan (π/2)) – π/4) – (-1/2 (1/tan (π/4)) – π/8)
    But clearly it is impossible and a math error to have tan π/2 or 90° so im not sure how to progress from there. The answer in the book is (4 – π)/8.
    Thanks for any help!
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  2. #2
    MHF Contributor
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    Maybe try the identity \cot(2x)=\frac{\cot^2(x)-1}{2\cot(x)}
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