A Hydraulic Cylinder on an Industrial Machine Pushes a Steel $( 0 \leq x \leq 4 )$

Multiple Choice

A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet $( 0 \leq x \leq 4 )$ , where the variable force required is $F ( x ) = 3000 x e ^ { - x }$ pounds. Find the work done in pushing the block the full 4 feet through the machine. Round your answer to three decimal places.

A) $2725.265 \mathrm { ft } . \mathrm { lbs }$
B) $2890.106 \mathrm { ft } . \mathrm { lbs }$
C) $1655.749 \mathrm { ft } . \mathrm { lbs }$
D) $2839.235 \mathrm { ft } . \mathrm { lbs }$
E) $3219.788 \mathrm { ft }$ .lbs