Hooke's law (confirmation if I did it right)

[mathnoobie]

Homework Statement

Seven and one half foot pounds of work is required to compress a spring 2 inches from its natural length. Find the work required to compress the spring an additional one-half inch

Homework Equations

W=kd
W=∫f(x)dx

The Attempt at a Solution

7.5=W
∫kxdx from (0,1/6)
=(kx^(2))/2 from (0,1/6)
=k/72=7.5
K=540

∫(540x)dx from (4/24, 5/24)

The rest is just algebra that's irrelevant; did i set up the problem right?

 

[HallsofIvy]

Yes, that is correct.