Deriving the Elastic Energy Equation: How Do I Go from F=kx to F=1/2kx^2?

[davyvfr]

Homework Statement

Derive an equation for elastic energy, in terms of k and x. Show all steps.

Homework Equations

F=1/2kx^2

The Attempt at a Solution

I believe Force=1/2kx^2 is the answer but how would I show steps to get an elastic energy equation? Basically, going from F=kx, what steps do I need to take to go from that equation to the elastic energy equation.

 

[Delphi51]

You need to find the work done by the F = kx force as it compresses the spring (or as the spring pushes with that force on some other object). x will vary from 0 (meaning no compression or extension) to some final value X. It would be easy if F didn't vary with x. Since it does vary with x, you will have to use calculus or some kind of workaround. Perhaps you can find a definition of work involving the area under a force graph.