Integral from zero to 2pi of sqrt(2+2cost)

Integral from zero to 2pi of sqrt(2-2cost)

Printable View

- September 4th 2006, 02:52 PMTexasGirlIntegral of sqrt(2+2cost)
Integral from zero to 2pi of sqrt(2+2cost)

Integral from zero to 2pi of sqrt(2-2cost) - September 4th 2006, 03:37 PMTD!
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). - September 4th 2006, 03:40 PMThePerfectHacker
Welcome back TD!

- September 4th 2006, 03:43 PMTD!Quote:

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 :) - September 4th 2006, 03:53 PMTD!Quote:

Originally Posted by**galactus**

*u*will stay the same...

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 ;) - September 4th 2006, 04:12 PMgalactus
Yes, I know. An oversight on my part.