# Both limits of integration change to zero.

1. Jul 8, 2013

### cp255

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. Jul 8, 2013

### vanhees71

Better try $x=\sinh u$.

3. Jul 8, 2013

### verty

This is not the mistake though, the mistake is doing the change of limits in the wrong direction.

4. Jul 8, 2013

### cp255

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. Jul 8, 2013

### Ray Vickson

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