# An object with a mass of 5 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= x^2-3x+6 . How much work would it take to move the object over x in [2, 3], where x is in meters?

N=mg; \qquad F_k(x) = \mu_k(x).N#.
Workdone : ${W}_{\mathmr{if}} \setminus \equiv \setminus {\int}_{{x}_{i}}^{{x}_{f}} F \left(x\right) . \mathrm{dx} = \setminus {\int}_{{x}_{i}}^{{x}_{f}} \setminus {\mu}_{k} \left(x\right) . N d . x$
${W}_{23} = m g . \setminus {\int}_{2}^{3} \left({x}^{2} - 3 x + 6\right) . \mathrm{dx} = m g {\left[\setminus \frac{{x}^{3}}{3} - \frac{3}{2} {x}^{2} + 6 x\right]}_{2}^{3} = \frac{29}{6.} m g = \frac{29}{6} \setminus \times \left(5 k g\right) \setminus \times \left(9.8 m {s}^{- 2}\right)$
$= 236.83$ Joules.