Hookes law: Calculate the work done by compressing a spring

[x86]

Homework Statement

Hookes law: Calculate the work done by compressing a spring by x distance

Homework Equations

W = Fd
Ee = 1/2 k x^2
F = kx

The Attempt at a Solution

I've found two solutions, but only one is correct. I'm confused why it's the second one.

First formula I derived:
W = Fd
F = kx
d = x

Therefore W = kx^2

However, you can also use the elastic potential energy equation which is a modified version of the equation I made which is

W = 1/2 k x^2 - 0

So, why is it the second equation and not the first one? The way I see it, they sort of both are valid. What is wrong with the first one? Work is force * distance, and that's exactly what I'm doing.

 

[CAF123]

The spring force is a function of x, so W = Fd is not valid. You will have to do an integral.