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This one is not hard. :)

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- Jun 29th 2008, 11:31 AMKrizalidToday's calculation of integral #20
Find

This one is not hard. :) - Jun 29th 2008, 12:01 PMMathstud28
- Jun 29th 2008, 12:03 PMKrizalid
I'm not gonna tell ya if that's the right track or not, that's something you have to find out.

- Jun 29th 2008, 12:36 PMjavax
hey these kinds I solve with Dalamber criterion.

taking the gives so it converges because

but whatever, here integrals are required. So I'm out(Shake) - Jun 29th 2008, 12:40 PMwingless
It's easy to solve this using Mathstud's approach.

- Jun 29th 2008, 01:34 PMMathstud28
Ok this one is killing me, I am making a mistake somewhere!

This gives us

so we have

Now we know that

So now we see that

This implies that

So then

and finally

Now the first part of that is equivalent to

So we have

Which I do not think is correct (Angry).

Where am I going wrong? Is this anywhere near correct? - Jun 29th 2008, 01:57 PMDystopia
My initial thought was also to use the beta function, but it ends up being a bit messy. I think it's probably easier to use the formula

Setting x = 1/2 gives the result:

Mathstud: - Jun 29th 2008, 01:59 PMMathstud28
- Jun 29th 2008, 02:52 PMKrizalid
See here.

It wasn't messy, besides Gamma function is not stupid. (Sun) - Jun 29th 2008, 03:05 PMDystopia