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Question on integration of a gradient.

  1. Jun 17, 2011 #1
    Why

    [tex] \int_a^b \nabla T\; d\vec l \;=\; T(b)-T(a)[/tex]

    Why integration of a gradient is always path independent?
     
  2. jcsd
  3. Jun 17, 2011 #2

    Hootenanny

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    This is the essence of the gradient theorem, which is a generalisation of the fundamental theorem of calculus. One can prove the gradient theorem with a simple application of Stokes' theorem.
     
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