Compute the Integral $\int _ { 0 } ^ { 4 } \int _ { 0 } ^ { 8 } e ^ { x + y } \mathrm {~d} x \mathrm {~d} y$

Compute the integral. $\int _ { 0 } ^ { 4 } \int _ { 0 } ^ { 8 } e ^ { x + y } \mathrm {~d} x \mathrm {~d} y$

A) $e ^ { 8 } e ^ { 4 }$
B) $\left( e ^ { 8 } - 1 \right) \left( e ^ { 4 } - 1 \right)$
C) $e ^ { 12 } + 12$
D) $e ^ { 12 } - 12$
E) $\frac { e ^ { 4 } } { \left( e ^ { 5 } - 1 \right) }$

Correct Answer:

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