$\begin{array}{1 1}3799.29J\\3699.29J\\1799.29J\\2699.29J\end{array} $

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Answer : 3799.29J

The work is found by integrating the force over the distance.

$W=\int\limits_{x_i}^{x_f} F.ds$

For the force in this problem we have,

$W=\int\limits_0^l (a+bx-cx^2)dx$

$\;\;\;\;=ax+\large\frac{1}{2}$$bx^2-\large\frac{1}{3}$$cx^3\big|_0^l$

$\;\;\;\;=(13500N)(0.271m)+\large\frac{1}{2}$$(8170N/m)(0.271m)^2-\large\frac{1}{3}$$(24000N/m^2)(0.271m)^3$

$\;\;\;\;=3799.29J$

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