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## #1 2012-10-08 07:16:10

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 2012-10-08 07:26:16

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 2012-10-08 07:29:30

zetafunc.
Guest

### Re: Integral

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

## #4 2012-10-08 07:41:24

bobbym

Online

### 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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

## #5 2012-10-08 07:50:36

zetafunc.
Guest

### Re: Integral

These two integrals are identical...

## #6 2012-10-08 08:06:24

bobbym

Online

### Re: Integral

Checking them now.

Yes, they are the same.

In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

## #7 2012-10-08 11:02:37

anonimnystefy
Real Member

Online

### Re: Integral

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

Last edited by anonimnystefy (2012-10-08 11:02:52)

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