Both limits of integration change to zero.

[cp255]

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?

 

[vanhees71]

Better try x=\sinh u.

 

[verty]

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

 

[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.

 

[Ray Vickson]

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
\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.