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The Iterated Integral $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 2 } } \int _ { r } ^ { \sqrt { 4 - r ^ { 2 } } } r d z d r d \theta$

Question 134

Multiple Choice

The iterated integral $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 2 } } \int _ { r } ^ { \sqrt { 4 - r ^ { 2 } } } r d z d r d \theta$ is

A) $\frac { 8 \pi ( 2 - \sqrt { 2 } ) } { 7 }$
B) $\frac { 8 \pi ( 2 + \sqrt { 2 } ) } { 5 }$
C) $\frac { 8 \pi ( 2 - \sqrt { 2 } ) } { 5 }$
D) $\frac { 8 \pi ( 2 + \sqrt { 2 } ) } { 3 }$
E) $\frac { 8 \pi ( 2 - \sqrt { 2 } ) } { 3 }$

The Iterated Integral ∫02π∫02∫r4−r2rdzdrdθ\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 2 } } \int _ { r } ^ { \sqrt { 4 - r ^ { 2 } } } r d z d r d \theta∫02π​∫02​​∫r4−r2​​rdzdrdθ

Multiple Choice

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The Iterated Integral $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 2 } } \int _ { r } ^ { \sqrt { 4 - r ^ { 2 } } } r d z d r d \theta$

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