Find the Mass of the Lamina Bounded by the Graphs $y = e ^ { - x } , y = 0 , x = 0$

Multiple Choice

Find the mass of the lamina bounded by the graphs of the equations $y = e ^ { - x } , y = 0 , x = 0$ , and $x = 6$ for the density $\rho = k y ^ { 2 }$

A) $\frac { 1 } { 9 } \left( 1 - e ^ { 12 } \right) k$
B) $\frac { 1 } { 3 } \left( 1 - e ^ { 18 } \right) k$
C) $\frac { 1 } { 9 } \left( - 1 + e ^ { - 18 } \right) k$
D) $\frac { 1 } { 3 } \left( - 1 + e ^ { - 12 } \right) k$
E) $\frac { 1 } { 9 } \left( 1 - e ^ { - 18 } \right) k$