# Both limits of integration change to zero.

## Homework Statement

Integrate (1 + x2)1/2 from -∏ to ∏

## 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

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vanhees71
Gold Member
2019 Award
Better try $x=\sinh u$.

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

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 Helper
Dearly Missed

## Homework Statement

Integrate (1 + x2)1/2 from -∏ to ∏

## 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.