Integrability of f,g on [a,b] and its Implications

[krcmd1]

f,g integrable on [a,b]

how does
$$\\integral from a to b of (f- lamda*g)^2 = 0 imply<br /> <br /> (\\integral (fg))^(1/2) =< (\\int f^2)^(1/2)(\\int g^2)^(1/2) ?<br /> <br /> [\tex]<br /> <br /> Thank you!$$

 

[krcmd1]

I still clearly don't have the hang of Latex, either.

 

[ice109]

here's how it should look

how does
$$\int^b_a(f- \lambda g)^2 = 0 \rightarrow<br /> <br /> (\int(f*g))^{1/2} =< (\int f^2)^{1/2}(\int g^2)^{1/2} ?<br />$$