The force (in newtons) required to stretch a particular elastic cord x meters beyond its natural length is modeled by
F(x)=xln(1+x) for 0≤x≤2.
Work is the integral of force with respect to displacement.
Answer the following questions about the work done in stretching the cord from x=0 to x=2.
(a) Write an integral expression for the work W (in joules) required to stretch the cord from x=0 to x=2.
(b) Before computing W, determine which factor in the integrand you will differentiate first and which you will integrate first. Provide a clear justification tied to the relative complexity of derivatives and antiderivatives of the factors involved.
(c) Evaluate W exactly, showing all steps that arise from the strategic choice made in part (b).