The Iterated Integral $\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 4 } \int _ { 0 } ^ { 1 } r e ^ { z } d z d r d \theta$

Multiple Choice

The iterated integral $\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 4 } \int _ { 0 } ^ { 1 } r e ^ { z } d z d r d \theta$ is

A) $5 \pi ( e - 1 )$
B) $5 \pi ( e + 1 )$
C) $6 \pi ( e - 1 )$
D) $6 \pi ( e + 1 )$
E) $4 \pi ( e - 1 )$