How to integrate this conundrum?

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In summary, The conversation is about proving the statement ∫x/(1+cos^2(x)) = pi/(2*√2) by using a substitution and a specific technique involving trigonometric integrals. The participants are discussing different methods and asking for help.
  • #1
I<3Gauss
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Does anyone know how to prove the following statement? I haven't messed with integrals for awhile and I have to say that I am kind of rusty on this. From initial attempts, it seems the integral on the left is not something you can integrate directly... Maybe Taylor Expansion of cos^2(x) would help?

∫x/(1+cos^2(x)) = pi/(2*√2) (integrated from pi to 0)

Thanks guys!
 
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  • #2
So you're asking for [tex]\displaystyle\int\limits_0^\pi\left(\dfrac{x\cdot dx}{1+\cos^2\left(x\right)}\right)[/tex]? My first thought was substitute [tex]u=\dfrac\pi2-x[/tex] and doing something like averaging out the results. Anyone?

EDIT: GRRR ... why isn't there a \mathrm on here?
 
  • #3
Whovian, What gave you the idea to make such a substitution? What technique are you using?
 
  • #4
It's just a substitution that helps with a lot of trig integrals from 0 to pi/2.
 

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