The Iterated Integral Is

A) $\frac { 2 ( 4 - \sqrt { 2 } ) } { 3 }$

Multiple Choice

The iterated integral $\int _ { 0 } ^ { \frac { \pi } { 4 } } \int _ { 2 \sin \theta } ^ { 2 \cos \theta } \int _ { 0 } ^ { r \sin \theta } r \cos ( \theta ) d z d r d \theta$ is

A) $\frac { 2 ( 4 - \sqrt { 2 } ) } { 3 }$
B) $\frac { 2 ( 4 + \sqrt { 2 } ) } { 5 }$
C) $\frac { 2 ( 4 - \sqrt { 2 } ) } { 5 }$
D) $\frac { 2 ( 4 + \sqrt { 2 } ) } { 15 }$
E) $\frac { 2 ( 4 - \sqrt { 2 } ) } { 15 }$