Integral from zero to 2pi of sqrt(2+2cost)
Integral from zero to 2pi of sqrt(2-2cost)
Switching to the the half angle using the right formula will make this a piece of cake:
The 2-2 will now disappear to get:
In the same way, but using the other formula, you'll find:
Be careful with the absolute values though, when using this for definite integration:
These too should be doable now, I'll let you finish. To check: you should find 8 (twice).
I kept hanging arround, just not as frequent as I once did (though that didn't last long either).Originally Posted by ThePerfectHacker
When I come arround, the threads I'd usually reply to are already answered (I only check a few forums briefly actually) - this one wasn't
I don't think the limits for u will stay the same...Originally Posted by galactus
Also: this method is fine for indefinite integration, but you have to be carefull when using it for definite integrals. This substitution is only valid on (-pi,pi) and the interval of integration is [0,2pi]. This can be resolved by noticing the symmetry in the function, but it makes it a bit more complicated of course