# An object with a mass of 1 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 3x^2-2x+12 . How much work would it take to move the object over #x in [1, 3], where x is in meters?

Feb 13, 2016

$W = 412 , 02 J$

#### Explanation:

$W = {\int}_{1}^{3} m g \cdot \left(3 {x}^{2} - 2 x + 12\right) \cdot d x$
$W = m g {\int}_{1}^{3} \left(3 {x}^{2} - 2 x + 12\right) \cdot d x$
$W = m g {\left[3 \cdot {x}^{3} / 3 - 2 \cdot {x}^{2} / 2 + 12 x\right]}_{1}^{3}$
$W = m g \left[\left[27 - 9 + 36\right] - \left[1 - 1 + 12\right]\right]$
$W = m g \left[42\right]$
$W = 1 \cdot 9 , 81 \cdot 42$
$W = 412 , 02 J$