The force applied against a moving object travelling on a linear path is given by F(x)= x^2+4x. How much work would it take to move the object over x in [0, 4] ?

Sep 18, 2016

I found: $53. \overline{3} J$
$W = {\int}_{{x}_{1}}^{{x}_{2}} F \left(x\right) \mathrm{dx} = {\int}_{0}^{4} \left({x}^{2} + 4 x\right) \mathrm{dx} =$
$= {x}^{3} / 3 + {\cancel{4}}^{2} {x}^{2} / \cancel{2} =$ evaluated between $0$ and $4$:
$= \left({4}^{3} / 3 + 2 \cdot {4}^{2}\right) - 0 = \frac{160}{3} J = 53. \overline{3} J$