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Solve the Problem dxd x For the Volume of the Region Enclosed by the Paraboloids

Question 172

Multiple Choice

Solve the problem.
-Write an iterated triple integral in the order dz dy dxd x for the volume of the region enclosed by the paraboloids z=8x2y2z = 8 - x ^ { 2 } - y ^ { 2 } and z=x2+y2z = x ^ { 2 } + y ^ { 2 } .


A) 228x28x28x2y2dy2dydx\int _ { - 2 } ^ { 2 } \int _ { - \sqrt { 8 - x ^ { 2 } } } ^ { \sqrt { 8 - x ^ { 2 } } } \int ^ { 8 - x ^ { 2 } - y ^ { 2 } } d y ^ { 2 } d y d x
B) 224x24x2x2+y28x2y2dzdydx\int _ { - 2 } ^ { 2 } \int _ { - \sqrt { 4 - x ^ { 2 } } } ^ { \sqrt { 4 - x ^ { 2 } } } \int _ { x ^ { 2 } + y ^ { 2 } } ^ { 8 - x ^ { 2 } - y ^ { 2 } } d z d y d x
C) 224x24x2x2+y24x2y2dzdydx\int _ { - 2 } ^ { 2 } \int _ { - \sqrt { 4 - x ^ { 2 } } } ^ { \sqrt { 4 - x ^ { 2 } } } \int _ { x ^ { 2 } + y ^ { 2 } } ^ { 4 - x ^ { 2 } - y ^ { 2 } } d z d y d x
D) 228x28x2x2+y24x2y2dzdydx\int _ { - 2 } ^ { 2 } \int _ { - \sqrt { 8 - x ^ { 2 } } } ^ { \sqrt { 8 - x ^ { 2 } } } \int _ { x ^ { 2 } + y ^ { 2 } } ^ { 4 - x ^ { 2 } - y ^ { 2 } } d z d y d x

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