# I Corollaries of the fundamental integral theorems

1. May 19, 2017

### Pushoam

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. May 19, 2017

### vanhees71

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!

3. May 19, 2017

### Pushoam

o.k.
Thank you.

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