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I am having trouble with this "simple" problem involving these two theorems:

Find the value of the integral (A dot da) over the surface s, where A = xi - yj + zk and S is the closed surface defined by the cylinder c^2 = x^2 + y^2. The top and bottom of the cylinder are z= 0 and z=d.

From common sense, integrating circular layers from z=0 to z=d should give the volume of a cylinder. The book doesn't have any sample problem so I don't know which theorem to apply, and how.

Here's a more complicated question:

Find the value of the integral (curl A da) over the surface s, where A = yi + zj + xk and S is the closed surface defined by the paraboloid z=1-x^2-y^2 where z >=0

I appreciate any help.

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# Homework Help: Gauss' Theorem/Stokes' theorem

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