letfandgbe integrable functions on [a,b]. Show that

$\displaystyle |\int_{a}^{b} fg| \leq {{({\int_{a}^{b}} f^{2})}^{1/2}{{({\int_{a}^{b}} g^{2})}^{1/2}$

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- Aug 1st 2010, 01:44 PMrondo09integrability
let

*f*and*g*be integrable functions on [a,b]. Show that

$\displaystyle |\int_{a}^{b} fg| \leq {{({\int_{a}^{b}} f^{2})}^{1/2}{{({\int_{a}^{b}} g^{2})}^{1/2}$ - Aug 1st 2010, 03:37 PMTheEmptySet
This is the Cauchy-Schwars inequality or a special case of Holders inequality when p=q=2. Try a Google search for either of these topics.

- Aug 2nd 2010, 01:27 AMHallsofIvy
rondo09, Did you notice the "edit" button at the bottom of your posts? If you mistype a post, edit it rather than starting a new thread.