3. (10 pts) (a) Describe the Divergence Theorem. (b) Let F = xy i' + xy...

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3. (10 pts) (a) Describe the Divergence Theorem. (b) Let F = xy i' + xy ] + (x + y)z k and let S be the surface bounding the solid cylinder E defined by x + y <4, and 0 z <1. Assume that the surface S is oriented outward, evaluate 7.13. Hint: Use the divergence Theorem first, then find the projection of the solid cylinder on xy-plane. Directly solving the surface integral is very difficulty. 3. (10 pts) (a) Describe the Divergence Theorem. (b) Let F = xy i' + xy ] + (x + y)z k and let S be the surface bounding the solid cylinder E defined by x + y <4, and 0 z <1. Assume that the surface S is oriented outward, evaluate 7.13. Hint: Use the divergence Theorem first, then find the projection of the solid cylinder on xy-plane. Directly solving the surface integral is very difficulty.

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a The Divergence Theorem also known as Gausss Theorem relates the flux of a vector field across a cl... View the full answer