# The force applied against a moving object travelling on a linear path is given by F(x)= 2x^3+x. How much work would it take to move the object over x in [2, 4] ?

Aug 14, 2016

126J

#### Explanation:

Provided it's a conservative force

$W = {\int}_{{x}_{1}}^{{x}_{2}} F \mathrm{dx}$

$= {\int}_{2}^{4} \left(2 {x}^{3} + x\right) \mathrm{dx} = {\left[\frac{1}{2} {x}^{2} \left({x}^{2} + 1\right)\right]}_{2}^{4}$

=1/2(4)^2(4^2+1) - 1/2(2)^2(2^2+`1)

$= 8 \left(17\right) - 2 \left(5\right) = 126$