UCI
MATH 2E -
Quiz 1
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Quiz 1 10 16 14 Math 2E Discussion Prof Laure Giovangigli Name Instructions Show all your work and simplify your answers completely No calculators notes books etc may be used during the quiz Student ID Number E zdV where E is enclosed by the paraboloid z x2 y2 and the plane 1 Evaluate cid 82 cid 82 cid 82 z 4 Solution 1 cid 90 cid 90 cid 90 4 cid 90 cid 90 1 2 zdzdA R x2 y2 R 16 x2 y2 dA where R is the region that is of interest You can think of it as the projection or shadow that the solid is casting down to the x y plane That region in this case is x2 y2 4 or a circle of radius 2 Using polar coordinates we have 16 r4 rdrd cid 90 2 cid 90 2 cid 90 2 0 0 1 2 0 16r r5dr cid 12 cid 12 cid 12 cid 12 r 2 r 0 8r2 1 6 r6 64 3
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