For a positive number $a$, the function $f ( x ) = \int _ { 0 } ^ { x } ( a - t ) e ^ { t } \, d t$ has a maximum value of 32. Find the area enclosed by the curve $y = 3 e ^ { x }$ and the two lines $x = a$ and $y = 3$. [4 points]
For a positive number $a$, the function $f ( x ) = \int _ { 0 } ^ { x } ( a - t ) e ^ { t } \, d t$ has a maximum value of 32. Find the area enclosed by the curve $y = 3 e ^ { x }$ and the two lines $x = a$ and $y = 3$. [4 points]