Integrate the Function F Over the Given Region $f ( x , y ) = y ^ { 2 } e ^ { x ^ { 4 } }$

Multiple Choice

Integrate the function f over the given region.
- $f ( x , y ) = y ^ { 2 } e ^ { x ^ { 4 } }$ over the triangular region in the first quadrant bounded by the lines $x = y / 2 , x = 1 , y = 0$

A) $\frac { 8 } { 3 } ( \mathrm { e } - 1 )$
B) $8 ( e + 1 )$
C) $\frac { 2 } { 3 } ( \mathrm { e } - 1 )$
D) $\frac { 2 } { 3 } \mathrm { e }$