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Both limits of integration change to zero.

  1. Jul 8, 2013 #1
    1. The problem statement, all variables and given/known data

    Integrate (1 + x2)1/2 from -∏ to ∏

    2. Relevant equations

    3. The attempt at a solution

    I substiuted x = tan(theta) but when I went to change the limits of integration I got 0 and 0. What am I doing wrong?
  2. jcsd
  3. Jul 8, 2013 #2


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    Better try [itex]x=\sinh u[/itex].
  4. Jul 8, 2013 #3


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    This is not the mistake though, the mistake is doing the change of limits in the wrong direction.
  5. Jul 8, 2013 #4
    Oh so I should have changed the limits to arctan(pi) and arctan(-pi). I'm used to changing them for regular substitution when you can just plug the limits straight in instead of having to solve for x first.
  6. Jul 8, 2013 #5

    Ray Vickson

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    Use the fact that the integrand is even, to get
    [tex]\int_{-\pi}^{\pi} \sqrt{1+x^2} \, dx = 2 \int_0^{\pi} \sqrt{1+x^2} \, dx.[/tex]
    This type of issue comes up a lot when changing variables in defiinite integrals, so you need to be very aware of it.
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