see post #2 here. you should be able to finish up. it shows you how to find
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,
---------------------------------------
2.
Show that
Deduce that
Integrate the previous inequality and make substitutions to get, :
Admit the Wallis integral :
And find the value of