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## #1 2008-01-26 08:08:00

tony123
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### Evaluate Integral

Evaluate Integral

Last edited by tony123 (2008-01-26 08:08:58)

## #2 2008-01-26 08:18:43

JaneFairfax
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### Re: Evaluate Integral

Krizalid, ¿dónde estás?

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

## #3 2008-01-26 12:38:50

Krizalid
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### Re: Evaluate Integral

Hola, jaja

Ya está resuelta en aquél foro. (I'm not gonna post the URL for not makin' SPAM.)

Tony: you should be patient, post your problems in one forum first, if you see that it's not solved, try with another ones.

munnaiit
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## #5 2008-05-01 09:51:58

moxiuming
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### Re: Evaluate Integral

let sinx=t for all x in [0,pi/2],then we got cosx=sqrt(1-x^2).so,(sinx)^25/[(sinx)^25+(cosx)^25]=t^25/[t^25+(\sqrt (1-x^2))]25=f(t).we can get the extreme values of f(t) as follows:
1.find f'(t);
2.find t such that f'(t)=0;for example t1,t2;
3.f(t1),f(t2) is the maxium and inum
4.estimate the integral by the extreme value.

## #6 2008-10-12 02:03:50

sce1912
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### Re: Evaluate Integral

The 25's look scary but it isn't actually that difficult to show that

Proof:

Let

Using the substitution

we have

Hence

Interestingly, this method is independant of the powers of sin and cos
so for all real n

Last edited by sce1912 (2008-10-12 02:26:51)