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Evaluate the Integral In Spherical Coordinates

Question 11

Essay

Evaluate the integral 4416y216y216x2y216x2y21x2+y2+z2dzcdxdy\int _ { - 4 } ^ { 4 } \int _ { - \sqrt { 16 - y ^ { 2 } } } ^ { \sqrt { 16 - y ^ { 2 } } } \int _ { - \sqrt { 16 - x ^ { 2 } - y ^ { 2 } } } ^ { \sqrt { 16 - x ^ { 2 } - y ^ { 2 } } } \frac { 1 } { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } d z c d x d y in spherical coordinates.

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