# The force applied against an object moving horizontally on a linear path is described by F(x)=x^3+ 3 . By how much does the object's kinetic energy change as the object moves from  x in [ 3, 5 ]?

Mar 9, 2016

${W}_{F} = \Delta K E = {\left[\frac{x \left({x}^{3} - 12\right)}{4}\right]}_{3}^{5} = 130 J$
${W}_{F} = \Delta K E = \frac{1}{2} m \Delta {v}^{2}$
Now ${W}_{F} = \int F \cdot \mathrm{dr} = {\int}_{3}^{5} F \cdot \mathrm{dx} = {\int}_{3}^{5} {x}^{3} + 3 \cdot \mathrm{dx}$
${W}_{F} = {\left[\frac{x \left({x}^{3} - 12\right)}{4}\right]}_{3}^{5} = 130 J$