Math Is Fun Forum

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.

zetafunc.

Guest

Re: Integral

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

zetafunc.

Guest

Re: Integral

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Integral

Hi;

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

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zetafunc.

Guest

Re: Integral

These two integrals are identical...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Integral

Checking them now.

Yes, they are the same.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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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