how to calulate this :

it seems easy but i wonder how it is tricky to solve it.

i planned several approaches but all of them failed. i think the answer should be someting similar to .(Headbang)

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- October 23rd 2008, 07:43 AMtoraj58how to calculate this integral!!!
how to calulate this :

it seems easy but i wonder how it is tricky to solve it.

i planned several approaches but all of them failed. i think the answer should be someting similar to .(Headbang) - October 23rd 2008, 07:48 AMJhevon
see post #2 here. you should be able to finish up. it shows you how to find

- October 23rd 2008, 09:47 AMtoraj58
yeah;

that was cool solution.

it was realy nice for me to use double integral trick and then benefit from solving the problem in Polar Coordinates that was undeniably easy.

so the answer is : - October 23rd 2008, 06:46 PMJhevon
- October 23rd 2008, 06:54 PMChris L T521
- October 23rd 2008, 10:28 PMMoo
And how do you know that ?

_____________________________________

Here is a few other ways.

**1.**

Consider

Find

Let

Show that

Integrate this latter formula.

Find an expression for with respect to f(x).

Show that

Conclude :

Since the integrand is even,

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**2.**

Show that

Deduce that

Integrate the previous inequality and make substitutions to get, :

Admit the Wallis integral :

And find the value of - October 24th 2008, 12:24 PMtoraj58
thanks for alternative solutions.(Clapping)