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**zetafunc.****Guest**

"(i) Use the substitution x = 2 - cosθ to evaluate the integral

.(ii) Show that, for a < b,

where

and ."I have done the first part and got

which is correct (according to WolframAlpha). But the second part of the question confuses me. I have done this:

Let x = (b - a) - cosθ, then dx = sinθdθ

and I have ended up with this:

but I do not know where to go from here. Help would be appreciated.

**zetafunc.****Guest**

Hmm, I am skeptical about that last line. According to W|A it is giving me a horrendous-looking solution.

**zetafunc.****Guest**

Never mind, forget W|A, it is unable to solve the problem so I do not trust its solution.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,466

Hi;

Alpha has a time limit. I do not think those two integrals are the same so something is wrong somewhere.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

These two integrals are identical...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,466

Checking them now.

Yes, they are the same.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Where can you get with the substitution x=(b-a)-a*cos(theta)?

*Last edited by anonimnystefy (2012-10-07 12:02:52)*

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