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The Iterated Integral 0π202016r2r2dzdrdθ\int _ { 0 } ^ { \frac { \pi } { 2 } } \int _ { 0 } ^ { 2 } \int _ { 0 } ^ { \sqrt { 16 - r ^ { 2 } } } r ^ { 2 } d z d r d \theta

Question 103

Multiple Choice

The iterated integral 0π202016r2r2dzdrdθ\int _ { 0 } ^ { \frac { \pi } { 2 } } \int _ { 0 } ^ { 2 } \int _ { 0 } ^ { \sqrt { 16 - r ^ { 2 } } } r ^ { 2 } d z d r d \theta is


A) 2π(4π33) 5\frac { 2 \pi ( 4 \pi - 3 \sqrt { 3 } ) } { 5 }
B) 2π(4π+33) 5\frac { 2 \pi ( 4 \pi + 3 \sqrt { 3 } ) } { 5 }
C) 2π(4π33) 3\frac { 2 \pi ( 4 \pi - 3 \sqrt { 3 } ) } { 3 }
D) 2π(4π+33) 3\frac { 2 \pi ( 4 \pi + 3 \sqrt { 3 } ) } { 3 }
E) 2π(4π33) 7\frac { 2 \pi ( 4 \pi - 3 \sqrt { 3 } ) } { 7 }

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