# The force applied on a moving object with a mass of 1 kg  on a linear path is given by F(x)=2x +3. How much work would it take to move the object over x in [1,2] ?

Apr 9, 2016

$W = 10 - 4 = 6 J$

#### Explanation:

$W = {\int}_{a}^{b} F \left(x\right) \cdot d x$

$W = {\int}_{1}^{2} \left(2 x + 3\right) d x = | 2 \cdot {x}^{2} / 2 + 3 x {|}_{1}^{2} = | {x}^{2} + 3 x {|}_{1}^{2}$

$W = \left({2}^{2} + 3 \cdot 2\right) - \left({1}^{2} + 3 \cdot 1\right)$

$W = \left(4 + 6\right) - \left(1 + 3\right)$

$W = 10 - 4 = 6 J$