Let be a vector field on with continuous partial derivatives, and a smooth orientable surface. Show that

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- Apr 17th 2010, 10:35 PMBruno J.Surface integral
Let be a vector field on with continuous partial derivatives, and a smooth orientable surface. Show that

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- May 21st 2010, 01:51 PMAllanCuz
I'd go to the definition of the divergence theorem.

Let's multiply through and examine the first component

Note that,

Represents the integral of the derivative of P with respect to x. Which means, we take the derivative and then integrate back to our original function. This means,

Thus,

- May 23rd 2010, 08:57 AMBruno J.
The surface doesn't need to be closed, in which case you cannot use the divergence theorem!