This question applies to finding the amount of work done.
Let's say I did an experiment where I pulled a spring. Let 'x' be the distance I pulled the string and f(x) be the force required to pull the ptring.
The result of the experiment is:
x (Meters):1,2,3,4,5,6,7,8,9,10
f(x) (Newtons):2,3,4,5,6,7,8,8,10,11
If I was to graph the data, I would get a linear line. To get the total amount of work done, wouldn't I just have to multiply the final distance
by the final amount of force (required to pull the spring)?
After all W = Force * Distance.
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If I were to graph the CHANGE in distance (delta X) against the amount of force required, would I still have to divide by 2?