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Vector Integral


The following vector integrals are related to the curl theorem. If

 F=cxP(x,y,z),
(1)

then

 int_CdsxP=int_S(daxdel )xP.
(2)

If

 F=cF,
(3)

then

 int_CFds=int_Sdaxdel F.
(4)

The following are related to the divergence theorem. If

 F=cxP(x,y,z),
(5)

then

 int_Vdel xFdV=int_SdaxF.
(6)

Finally, if

 F=cF,
(7)

then

 int_Vdel FdV=int_SFda.
(8)

See also

Curl Theorem, Divergence Theorem, Gradient Theorem, Green's Identities, Line Integral, Surface Integral, Volume Integral

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Cite this as:

Weisstein, Eric W. "Vector Integral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/VectorIntegral.html

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