# The force applied against an object moving horizontally on a linear path is described by F(x)= cospix+1 . By how much does the object's kinetic energy change as the object moves from  x in [ 2, 5 ]?

Feb 12, 2016

$\Delta {E}_{k} = 3 J$

#### Explanation:

$\text{Work done by Force is equal to changing kinetic energy in interval(2,5)}$
$\Delta {E}_{k} = W = {\int}_{2}^{5} \left(\cos \pi x + 1\right) d x$
$\Delta {E}_{k} = {\int}_{2}^{5} \left(\cos \pi x\right) d x + {\int}_{2}^{5} d x$
$\Delta {E}_{k} = {\left[- \frac{1}{\pi} \sin \pi x\right]}_{2}^{5} + {\left[x\right]}_{2}^{5}$
$\Delta {E}_{k} = \left[- \frac{1}{\pi} \sin 5 \pi - \left(- \frac{1}{\pi} \sin 2 \pi\right)\right] + \left(5 - 2\right)$
$\Delta {E}_{k} = \left[- \frac{1}{\pi} 0 - \left(- \frac{1}{\pi} 0\right)\right] + 3$
$\Delta {E}_{k} = 3 J$