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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
- Administrator
Offline
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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#6 2012-10-08 08:06:24
- bobbym
- Administrator
Offline
Re: Integral
Checking them now.
Yes, they are the same.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#7 2012-10-08 11:02:37
- anonimnystefy
- Real Member
Offline
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)
The limit operator is just an excuse for doing something you know you can't.
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