For f nonnegative and continuous on [0,1], prove.
[tex] \left( \int f \right) ^2 < \int f^2[/tex]
With the limits from 0 to 1.
The Attempt at a Solution
I was trying to use Upper sums, i.e.
[tex]\inf \sum \Delta x_i M_i(f^2) = \inf \sum \Delta x_i (M_i(f))^2[/tex]
and then compare this to [tex]\inf \left[ \sum \Delta x_i M_i(f) \right] ^2 [/tex]
Am I in the correct way to prove it?
Why does f is required to be continuous, I didn't use this fact!