# The force applied against a moving object travelling on a linear path is given by F(x)= sinx + 1 . How much work would it take to move the object over x in [ 0, (5pi) / 8 ] ?

Aug 4, 2016

Here work done by the force is
$W = {\int}_{0}^{\frac{5 \pi}{8}} F \left(x\right) \mathrm{dx}$

$\implies W = {\int}_{0}^{\frac{5 \pi}{8}} \left(\sin x + 1\right) \mathrm{dx}$

$\implies W = {\left[- \cos x + x\right]}_{0}^{\frac{5 \pi}{8}}$

$\implies W = \left(- \cos \left(\frac{5 \pi}{8}\right) + \left(\frac{5 \pi}{8}\right)\right) - \left(- \cos \left(0\right) + 0\right)$

$\implies W = 0.38 + 1.96 + 1 = 3.34$