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**tony123****Member**- Registered: 2007-08-03
- Posts: 189

Evaluate Integral

*Last edited by tony123 (2008-01-25 09:08:58)*

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Krizalid, ¿dónde estás?

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**Krizalid****Member**- Registered: 2007-03-09
- Posts: 51

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.

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**munnaiit****Member**- Registered: 2008-02-05
- Posts: 0

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**moxiuming****Member**- Registered: 2008-04-20
- Posts: 7

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.

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**sce1912****Member**- Registered: 2008-10-08
- Posts: 5

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

Proof:

Let

Using the substitution

we have

Adding gives

Hence

:)

Interestingly, this method is independant of the powers of sin and cos

so for all real n

*Last edited by sce1912 (2008-10-11 03:26:51)*

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