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Definite Integral with trig

  1. Jan 24, 2012 #1
    1. The problem statement, all variables and given/known data

    [itex]\int\stackrel{tan(8)}{tan(1)}\frac{dx}{x^{2}+1}[/itex]

    2. Relevant equations



    3. The attempt at a solution

    [itex]\int\stackrel{tan(8)}{tan(1)}\frac{dx}{x^{2}+1}[/itex]


    [itex]tan^{-1}x|\stackrel{tan(8)}{tan(1)}[/itex]


    [itex]tan^{-1}(tan(8))-tan^{-1}(tan(1))[/itex]


    [itex]8-1=7[/itex]


    I'm fine with this, but my instructor said "Hint: The answer isn't 7."

    What did I do wrong here?


    As a side note, is there a better way to type a def. integral in LaTeX?
     
    Last edited: Jan 24, 2012
  2. jcsd
  3. Jan 24, 2012 #2

    SammyS

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    Look at the value of tan(8 radians). It's negative.

    If u < 0, tan-1(u) < 0 .

    Also, tan-1(tan(θ)) = θ, only if [itex]\displaystyle \ -\frac{\pi}{2}<\theta<\frac{\pi}{2}\,.[/itex] The number, 8, is not in that interval.
     
  4. Jan 25, 2012 #3
    Thanks a lot, I got it now:
    tan-1(tan(θ)) =8-3pi
    tan-1(tan(1)) = 1
     
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