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Math Help - Multivariable differential with integral questions

  1. #1
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    Multivariable differential with integral questions

    Multivariable differential with integral questions-questionsn.jpg

    I am stucked after the last line. It seems there is no way to make the equality hold.

    Thank you very much.
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  2. #2
    Super Member girdav's Avatar
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    You missed some terms : for example we have \displaystyle\int_{a_2}^{x_2}\dfrac{\partial f(x_1,t,a_3,\ldots,a_n)}{\partial x_2}\mathrm{d}t= f(x_1,x_2,a_3,\ldots,a_n)-f(x_1,a_2,a_3,\ldots,a_n).
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  3. #3
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    I did have one more question. I deduced that from the fundamental theorem.

    d/dx int (a to x) f(t)dt = f(x)

    with no - f(a) entering.

    While it appears here ?

    Thanks a lot.
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  4. #4
    Super Member girdav's Avatar
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    Indeed it doesn't appear in the first term, but it appear in the others because it's not the same differentiation (here it is differentiation under the symbol \int).
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  5. #5
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    Thanks a lot I got it now.
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