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Calculate for each of the following. Looked at the right way, all are quite easy and some are even trivial.
(a) ; is the solid sphere .
(b) as in part (a).
(c) ; S is the solid sphere .
(d) is the cube .
(e) is the tetrahedron cut from the first octant by the plane .
(f) as in part (a).
(g) ; S is the solid cylinder .
(a) Show that .
(b) Show, by using the parametrization , that , where C is the unit circle.
(c) Why doesn't this contradict Green's Theorem?
(a) In order to find , we will differentiate , while treating like a constant
Note: Use the quotient rule for differentiation
Note: Use the power rule for differentiation
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