The iterated integral $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 2 } \rho ^ { 2 } \sin ( \varphi ) d \rho d \varphi d \theta$ is

A) $\frac { 64 \pi } { 3 }$
B) $\frac { 32 \pi } { 3 }$
C) $\frac { 16 \pi } { 3 }$
D) $\frac { 8 \pi } { 3 }$
E) $\frac { 4 \pi } { 3 }$

Question

The iterated integral $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 2 } \rho ^ { 2 } \sin ( \varphi ) d \rho d \varphi d \theta$ is

A) $\frac { 64 \pi } { 3 }$
B) $\frac { 32 \pi } { 3 }$
C) $\frac { 16 \pi } { 3 }$
D) $\frac { 8 \pi } { 3 }$
E) $\frac { 4 \pi } { 3 }$

Quizplus · Accepted Answer

The Answer of The iterated integral $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 2 } \rho ^ { 2 } \sin ( \varphi ) d \rho d \varphi d \theta$ is

A) $\frac { 64 \pi } { 3 }$
B) $\frac { 32 \pi } { 3 }$
C) $\frac { 16 \pi } { 3 }$
D) $\frac { 8 \pi } { 3 }$
E) $\frac { 4 \pi } { 3 }$

The Iterated Integral ∫02π∫0π∫02ρ2sin⁡(φ)dρdφdθ\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 2 } \rho ^ { 2 } \sin ( \varphi ) d \rho d \varphi d \theta∫02π​∫0π​∫02​ρ2sin(φ)dρdφdθ

The Iterated Integral $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 2 } \rho ^ { 2 } \sin ( \varphi ) d \rho d \varphi d \theta$