Not sure about Hooke's Law...?

This is part of my Calc2 homework that the professor hasn't discussed.

"If a spring needs 10lbs of work in order to keep it stretched 4 inches from it's natural length, how much work is need it to stretch it to 6 inches from it's natural length?"

According to the book, the best method is to use Hooke's Law ( ), but I'm having some trouble applying it.

I'm going to assume that the natural length is and stretching it inches would give me . The force needed to keep it here is denoted by , having .

So, would I have: , so that ?

If that's correct, then all that's left is the integral:

Thank you for your help!

Quote:

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"If a spring needs 10lbs of work in order to keep it stretched 4 inches from it's natural length, how much work is need it to stretch it to 6 inches from it's natural length?"

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I think it should say, "10lbs of force."

In Hooke's law, you don't count the natural length, so 4 inches is the displacement of the spring's end from its equilibrium position. Thus, 10 = 4k, from where k can be found.

The work needed to stretch the spring to 6 inches from it's natural length is (up to the sign) .