A force of 750 pounds compresses a spring 3 inches from its natural length of 15 inches. Find the work done in compressing the spring an additional 3 inches.
They seem to want you to assume a lot. Not really sure why this is even a calc question.
On a force-distance graph, y = 750 when x = 3 and y = 0 when x = 0.
The integral of a force-distance graph gives you force*distance, or work.
So we have
$\displaystyle W(3) - W(0) = \int_{0}^{3} F(x)dx = Fd = 750*3 = 2250$
And we want
$\displaystyle W(6) - W(3)$
We know that W(0) is 0, so W(3) must be 2250.