# The force applied against a moving object travelling on a linear path is given by F(x)= 4x + 4. How much work would it take to move the object over x in [ 4 , 7] ?

Oct 17, 2017

I got $78 J$

#### Explanation:

In this case you have a variable force $F \left(x\right) = 4 x + 4$ that depends upon position $x$, so we need to use a small work to evaluate it at each position:

$\mathrm{dW} = F \left(x\right) \mathrm{dx}$

To get the entire amount along your entire displacement we can integrate the above expression to get the total work as:

$W = {\int}_{4}^{7} \left(4 x + 4\right) \mathrm{dx}$

integrating:

$W = {\cancel{4}}^{2} {x}^{2} / \cancel{2} + 4 x = 2 {x}^{2} + 4 x$ evaluated between $4 \mathmr{and} 7$:

$W = \left(2 \cdot {7}^{2} + 4 \cdot 7\right) - \left(2 \cdot {4}^{2} + 4 \cdot 4\right) = 78 J$