Then in the entire integrand, set , so that . The integral is then equivalent to
Note that by letting , we are enforcing an invertible substitution which would make it so that requires or . However, is positive over this first interval and negative over the second, so we can't ignore the absolute value.
So let's just assume the integral is being taken over a domain on which so that . This allows us to write
We can show pretty easily that
which means the integral above becomes
Back-substituting to get this in terms of is a bit of a nightmare, but you'll find that, since , we get
The exterior angles of a polygon all add to 360, if you need to find an exterior angle when given the number of sides and that all angles are equal you simply do: 360/ number of sides. When you need to find the exterior angle when given an interior angle, you do: 180- interior angle.