A force has the dependence Fx(x) = -kx^4 on the displacement x, where the constant k = 20.3 N/m^4. How much work does it take to change the displacement, working against the force, from 0.730 m to 1.35 m?

Answer 1

If you mean the spring force is
F(x) = - k x^4
the force you have to exert is the negative of that
then integral from x1 to x2 of
integral-F(x) dx
which is (1/5)k [ x2^5 - x1^5 ]

= (1/5) k [ 1.35^5 - .73^5 ]