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#1 2012-10-07 08:16:10

zetafunc.
Guest

Integral

"(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.

#2 2012-10-07 08:26:16

zetafunc.
Guest

Re: Integral

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

#3 2012-10-07 08:29:30

zetafunc.
Guest

Re: Integral

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

#4 2012-10-07 08:41:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Integral

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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#5 2012-10-07 08:50:36

zetafunc.
Guest

Re: Integral

These two integrals are identical...

#6 2012-10-07 09:06:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Integral

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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#7 2012-10-07 12:02:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Integral

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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