# A calculus problem by Hummus a

Calculus Level 4

let $$F:[0,\pi ]\rightarrow \mathbb{R}$$ be a smooth function with $$F(0)=F(\pi )=0$$

You're given that $$\displaystyle\int _{ 0 }^{ \pi }{ (F(x))^{ 2 } } dx=1$$

find the minimum value of $$\displaystyle\int _{ 0 }^{ \pi }{ \left (\dfrac { dF }{ dx } \right )^{ 2 } \, dx }$$

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