Suppose that 2 J of work is needed to stretch a spring from it's natural length of 30cm to a length of 42cm. How much work is needed to stretch the spring from 35cm to 40cm?

The answer is $\displaystyle \frac{25}{24}$.

The difference is 12cm, but Hooke's law is in meters, so I need to use .12. Accordingly I get 2=.12k just plugging into Hooke's law. k is $\displaystyle \frac{50}{3}$.

For the setup, I get:

$\displaystyle \int(\frac{50}{3})x dx$ The interval is supposed to be .05 to .10, but I can't get it to work for some reason. I get 1/16 as the answer, which is wrong.

If I don't convert to meters, I get $\displaystyle k=\frac{1}{6}$ with an interval of 5 to 10, and that yields an answer of $\displaystyle \frac{25}{4}$, also wrong.

What am I doing wrong?