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Both limits of integration change to zero.

  • Thread starter cp255
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  • #1
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Homework Statement



Integrate (1 + x2)1/2 from -∏ to ∏

Homework Equations





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?
 

Answers and Replies

  • #2
vanhees71
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Better try [itex]x=\sinh u[/itex].
 
  • #3
verty
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This is not the mistake though, the mistake is doing the change of limits in the wrong direction.
 
  • #4
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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.
 
  • #5
Ray Vickson
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Homework Statement



Integrate (1 + x2)1/2 from -∏ to ∏

Homework Equations





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?
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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