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I Corollaries of the fundamental integral theorems

  1. May 19, 2017 #1
    Can anyone please tell me significance of these corollaries of fundamental integral theorems?
    I can prove these corollaries but I don't understand why do we need to learn it?
    Do these corollaries have some physical significance?

    (a)$$\iiint_V(\nabla T)d^3 x=\oint_S T d\vec a$$
    here S is the surface bounding the volume V .
    (b)$$\iiint_V(\nabla \times\vec v)d^3 x= -\oint_S\vec v\times d\vec a$$,where S is the surface bounding the volume V .

    (c)$$\iint_S(\nabla T)\times d\vec a =-\oint_P T d\vec l$$ , where P is the boundary of the surface S.
  2. jcsd
  3. May 19, 2017 #2


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    It's sometimes useful in formulating integral laws in fluid dynamics. Be careful with these formulae. They are really safe only when used in Cartesian coordinates!
  4. May 19, 2017 #3
    Thank you.
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