Consider a spring that does not obey Hooke's law very faithfully. One end of the spring is fixed. To keep the spring stretched or compressed an amount x, a force along the x-axis with x-component F_x=kxbx²+cx³ must be applied to the free end. Here k=100N/m, b=700N/m², and c=12,000N/m³. Note that x>0 when the spring is stretched and x<0 when it is compressed.

a. How much work must be done to stretch this spring by 0.050 m from its unstretched length?

b. How much work must be done to compress this spring by 0.050 m from its unstretched length?