6.2.2—The area under the force–extension graph represents the work done

Work done by a changing force is the area under the force–extension graph, W=∫F dx; for a linear spring from zero, W=½Fx=½kx².

Use the loading path and the correct graph axes. The area represents energy transferred into elastic or other deformation stores.

A spring reaching 0.20 m under 40 N with a straight-line graph stores 4.0 J of elastic energy.

The area is not simply F×final extension unless force is constant; unloading can enclose a different area when energy is dissipated.