Help using Hooke's law to find work

[mathnoobie]

Homework Statement

Use Hooke's Law to determine the variable force in spring problem.

Eighteen foot-pounds of work is required to stretch a spring 4 inches from it's natural length. Find the work required to stretch the spring an additional 3 inches.

Homework Equations

W=∫f(x)dx
f=kd

The Attempt at a Solution

I set the work equal to 18 and the distance equal to 4.
so 18=4K, K=18/4
with this knowledge I set my function is (18/4)X
integrating
∫(18x/4)dx from 4 to 7
I get 9x(^2)/4
using the fundamental theorum of Calculus from 4 to 7
I get 74 1/4 (not sure of units, is it inches-pound)

 

[OldEngr63]

You need to start off recognizing that

W - W(t) = ∫₀^df(x) dx = ∫₀^d kx dx

If you will re-work the problem with this beginning, I think you will get a totally different outcome.