Final answer:
The work required to move an object from x=1 to x=5 in the presence of a force given by f(x)=4/x² along the x-axis is 16/5 units of work.
Step-by-step explanation:
The work required to move an object from x=1 to x=5 in the presence of a force given by f(x)=4/x² along the x-axis can be calculated by integrating the force function over the given interval. In this case, the force function is given as f(x) = 4/x². To calculate the work, we need to integrate the force function from x=1 to x=5:
Work = ∫1⁵ (4/x²) dx
Work = 4 ∫1⁵ (1/x²) dx
To integrate this function, we can use the power rule of integration:
Work = 4(-1/x)ᵢ_1__⁵
Substituting the limits of integration:
Work = 4[(-1/5)-(-1/1)]
Work = 4[(-1/5)+1]
Work = 4(4/5)
Work = 16/5
Therefore, the work required to move the object from x=1 to x=5 is 16/5 units of work.