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Math Help - [SOLVED] integrability of f and f^2

  1. #1
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    [SOLVED] integrability of f and f^2

    I need help with this problem.

    Let[tex] f(x)[\math] be a bounded function on [a,b]. Let B>0 and |f(x)| \leq B for \forall x \in [a,b]

    Show that U(f^2,P)-L(f^2,P) \leq 2B[U(f,P)-L(f,P)] for all partitions P of [a,b]
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  2. #2
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    Quote Originally Posted by akolman View Post
    Let  f(x) be a bounded function on [a,b]. Let B>0 and |f(x)| \leq B for \forall x \in [a,b]

    Show that U(f^2,P)-L(f^2,P) \leq 2B[U(f,P)-L(f,P)] for all partitions P of [a,b]
    Difference of two squares: \left|f^2(x_1) - f^2(x_2)\right| = |f(x_1) + f(x_2)|\,|f(x_1) - f(x_2)|\leqslant2B|f(x_1) - f(x_2)|.
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  3. #3
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    Ohh man! I can believe it! tank you very much!!
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