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Let E Be the Part of the Solid Ellipsoid x2+y2+4z29x ^ { 2 } + y ^ { 2 } + 4 z ^ { 2 } \leq 9

Question 69

Essay

Let E be the part of the solid ellipsoid x2+y2+4z29x ^ { 2 } + y ^ { 2 } + 4 z ^ { 2 } \leq 9 that lies in the first octant above
the plane z = 1.(a) Express the triple integral ZyzdV\iiint _ { Z } \frac { y } { z } d V as an iterated integral in rectangular coordinates.(b) Express the triple integral ZyzdV\iiint _ { Z } \frac { y } { z } d V as an iterated integral in cylindrical coordinates.(c) Express the triple integral ZyzdV\iiint _ { Z } \frac { y } { z } d V as an iterated integral in spherical coordinates.

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