Suppose S and E satisfy the conditions of the Divergence Theorem and f is a scalar function with continuous partial derivatives Prove that These surface and triple integrals of vector functions are vectors defined by integrating each component function SI vsav fn dS VfdV...

If c qicj c3 k is an arbitrary constant vector we define F c cifcjfc3 k Then af af div F div fc C ...

Suppose S and E satisfy the conditions of the Divergence Theorem and f is a scalar function

Question:

Suppose S and E satisfy the conditions of the Divergence Theorem and f is a scalar function with continuous partial derivatives.
Prove that SI vsav | fn dS = VfdV These surface and triple integrals of vector functions are vectors defined by integrating each component function.