A particle slides along a straight track under the influence of a position-dependent force given by
F(x)=kxe−x/L,0≤x≤5L,
where k and L are positive constants.
(a) Write an expression for the total work W done by the force in moving the particle from x=0 to x=5L.
(b) Evaluate W in closed form, expressing your answer in terms of k and L only.
(c) Suppose L is doubled while k remains fixed. Determine the factor by which the work changes and justify your conclusion algebraically.