Bunya-Calculus!

Calculus Level 4

If \[f(x)+g(x)+h(x)=2\]for all\[x \epsilon\mathbb{R}\] find the minimum value of the following expression

\[\int_{0}^{3/4}\left ( f(x)^{2}+g(x)^2+h(x)^2 \right )dx\]

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