Question

For a particular nonlinear spring the relationship between the magnitude of the applied for F and the resultant displacement x from equilibrium is given by the equation F=kx^2. What is the amount of work done by stretching the spring a distance x_0?

a)kx_0^2
b) 1/2 kx_0
c)1/2 kx_0^3
d) 1/3 kx_0^2
e)1/3 kx_0^3

W=1/2kx_i^2 -1/2kx_f^2 but I don't know what I would do with this equation. Can you please explain how I would solve this problem?

To get the work, you have to integrate the force as a function of x from zero displacement to Xo

(Integral of) k x^2 dx from 0 to Xo = (1/3) k (Xo)^3