Hooke's Law and Work; easy problem, I shouldn't have trouble, but I get it wrong

1. Oct 8, 2012

B3NR4Y

1. The problem statement, all variables and given/known data
A string of natural length 10 in. stretches 1.5 in. under a weight of 8-lb. Find the work done in stretching the spring from its natural length to a length of 14 in.

2. Relevant equations

W= \int_a^b \, f(x)dx

f(x)=kx

3. The attempt at a solution

8=k(\frac{3}{2})

k=\frac{16}{3}

W=\frac{16}{3} \int_0^4 \, xdx

W= \frac{16}{3} \, (\frac{1}{2} x^{2} |^{4}_{0})

\frac{2048}{9}