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## Homework Statement

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.

## Homework Equations

## 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!