Maximize The Difference!

Level pending

For all continuous functions \(f:[0,1]\rightarrow \mathbb{R}\), let

\[K_f=\int_0^1 x^2 f(x) ~\text{d}x\]

\[L_f=\int_0^1 x (f(x))^2~\text{d}x\]

The maximum value of \(K_f-L_f\) over all such functions can be represented as \(\dfrac a b\). Find \(a+b\).

×

Problem Loading...

Note Loading...

Set Loading...