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Math Help - Need help with a problem on Optimisation

  1. #1
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    Need help with a problem on Optimisation

    Please help me with finding the function u, which gives the minimal value of the integral from 0 to 1:

    Int(u'(x)^2+u(x))dx--> min

    with conditions:

    Int(u^2(x))dx=1 (integral is from 0 to 1)
    u'(0)=u'(1)=0

    Where u has a continuous derivative.
    Last edited by eduardos88; December 11th 2009 at 06:36 AM.
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  2. #2
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    Well i know e^x has a continuous derivative, so consider than function, just giving some input, maybe wrong.
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  3. #3
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    Quote Originally Posted by RockHard View Post
    Well i know e^x has a continuous derivative, so consider than function, just giving some input, maybe wrong.
    it is not so simple problem)
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  4. #4
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    That is a "calculus of variations" problem. Calculus of variations - Wikipedia, the free encyclopedia

    Do you know the corresponding "Euler-Lagrange" equation?
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