MATH 2E Study Guide - Final Guide: Parametric Surface, Iterated Integral, Divergence Theorem
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Problem 1: evaluate x + y = 2 and the cylinder y2 + z2 = 1 in the rst octant. E z dv, where e is bounded by the planes y = 0, z = 0, (cid:90)(cid:90)(cid:90) z3(cid:113) Problem 2: evaluate that lies above the xy-plane and has center the origin and radius 1. x2 + y2 + z2 dv, where h is the solid hemisphere. Problem 3: find the volume of the solid tetrahedron with vertices (0, 0, 0), (0, 0, 1), (0, 2, 0) and (2, 2, 0). 3 the half cone z =(cid:112)x2 + y2. Problem 4: find the volume of the solid above the paraboloid z = x2 + y2 and below. Problem 5: use the transformation x = u2, y = v2, z = w2 to nd the volume of the region bounded by the surface z = 1 and the coordinates planes. x + y +
