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Math Help - A problem involving integrable and continuous functions

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    A problem involving integrable and continuous functions

    Suppose that the functions h,g:[a,b]\mapto\mathbb{R} be continuous. Prove that \int^b_{a}\leq\sqrt{\int^b_{a}h^2}\sqrt{\int^b_{a}  g^2}
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    Quote Originally Posted by tttcomrader View Post
    Suppose that the functions h,g:[a,b]\mapto\mathbb{R} be continuous. Prove that \int^b_{a}\leq\sqrt{\int^b_{a}h^2}\sqrt{\int^b_{a}  g^2}
    There's a problem here. What's that first integral?

    -Dan
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    Quote Originally Posted by tttcomrader View Post
    Suppose that the functions h,g:[a,b]\mapto\mathbb{R} be continuous. Prove that \int^b_{a}\leq\sqrt{\int^b_{a}h^2}\sqrt{\int^b_{a}  g^2}
    Are you asking for a proof of the Cauchy-Schwartz inequality for continuous real functions on [a,b]?

    [int(h(x) g(x) dx, a,b)]^2<=int([h(x)]^2 dx, a,b) int([g(x)]^2 dx, a,b)

    RonL
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    I believe the way your prove it is by taking the limit of the Riemann sum. And since for all finite sums this inequality is true then it is true also for an infinite sum.*

    *)If a_n<= s then lim a_n <= s if it exists.
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    Quote Originally Posted by ThePerfectHacker View Post
    I believe the way your prove it is by taking the limit of the Riemann sum. And since for all finite sums this inequality is true then it is true also for an infinite sum.*

    *)If a_n<= s then lim a_n <= s if it exists.
    You don't have to, the proof works out of the box.

    RonL
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    Quote Originally Posted by CaptainBlack View Post
    You don't have to, the proof works out of the box.
    But! If you accept the standard Cauhy-Swartzh inequality for inner product spaces in general then there is nothing to it. However, he might want to use the algebraic Cauchy-Swartzh inequality and apply it ot integration.
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    I don't know what is going on with the coding, did I do something wrong? Why isn't my inequality showing up as it is?
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    Quote Originally Posted by tttcomrader View Post
    I don't know what is going on with the coding, did I do something wrong? Why isn't my inequality showing up as it is?
    There's a problem with the LaTeX. It's off-line until they fix it.

    -Dan
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