I think I have the solution. I'm going to use Hoelder inequality
Where
We see that
Hence
By Hoelder inequality we get
Which, you can easily see implies the inequality we were to prove
Any help with this prof is most wellcome.
Prove that, for any continuosly differentiable function f on [-phi, phi],
│ ∫[-phi, phi] f(t)cos(t) –f´(t) sin (t) dt│
≤ (2*phi)^½ * ({∫│f(t)^2 +│f´(t)│^2})^½
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