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Math Help - Why do you divide by 2 get get the area under a linear graph?

  1. #1
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    Why do you divide by 2 get get the area under a linear graph?

    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.


    ---
    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?
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  2. #2
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    Quote Originally Posted by Masterthief1324 View Post
    This question applies to finding the amount of work done....
    1. To answer the question in the headline: The area in question is a triangle with it's base on the x-axis and the height parallel to the y-axis.

    2. The area of every triangle is half of a rectangle:

    a_\Delta = \frac12 \cdot base \cdot height

    That's where the division by 2 comes from.
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