Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

Evaluate Integral

Evaluate Integral

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

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Evaluate Integral

Krizalid, ¿dónde estás?

Krizalid

Member

Registered: 2007-03-09

Posts: 51

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

Member

Registered: 2008-02-05

Posts: 0

Re: Evaluate Integral

moxiuming

Member

Registered: 2008-04-20

Posts: 7

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.

sce1912

Member

Registered: 2008-10-08

Posts: 5

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

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)