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    Integration : Fubini's Theorem

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    Use attached to solve the following question by integrating over an appropriate rectangle.

    Assume f is class C2 Prove the following theorem by Fubini's Theorem.

    Please see attachment.

    For f of class C2

    Left Hand side:

    Right Hand side:

    Use above to solve the following question by integrating over an appropriate rectangle.

    Assume f is class C2 Prove the following theorem by Fubini's Theorem.
    Theorem:
    Let be open and suppose f: is a class C2 function.
    Then for any i and j we have

    (Hint: Proceed by contradiction if the mixed partials are not equal at some point, apply (a) to show we can find a rectangle on which, )
    (a) Suppose is open and f: is continuous. If a and f(a) >0. there is δ>0 so that f(x) > 0 for all )

    © BrainMass Inc. brainmass.com February 24, 2021, 2:35 pm ad1c9bdddf
    https://brainmass.com/math/integrals/integration-fubinis-theorem-31024

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    Left Hand side:
    (*)
    Right ...

    Solution Summary

    An integral is found using Fubini's theorem.

    $2.19

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