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 .
And how do you know that ?
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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