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Math Help - Functions

  1. #1
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    Functions

    Prove that if f' and g' are continuous on a line interval [a,b] then
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by matty888 View Post
    Prove that if f' and g' are continuous on a line interval [a,b] then
    This is just the definition of integration by parts of a definite integral
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    Moo
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    Hello,

    Mathstud : I think he wants to demonstrate it



    \int_a^b f(x)g'(x)dx=? f(x)g(x)|_a^b -\int_a^b g'(x)f(x) dx

    Consider f(x)g(x)

    f(x)g(x)|_a^b = \int_a^b \left(f(x)g(x) \right)' dx

    What is the derivative for f(x)g(x)?

    Then by using the linearity of the integral, you'll get the result.
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