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Math Help - Area under a Curve

  1. #1
    Junior Member
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    Area under a Curve

    Hi

    Is it possible to find the area under a curve if all I have is the x and y co-ordinate? I.e. I dont have the equation if the curve, for example, I know that the y value for the beginning of my curve is 3 and the x-value for the end of my curve is 5.

    1.
    1..
    1...
    1....
    1.....
    1......
    1.......
    1........
    1..........
    1............
    1..............
    1................
    1..................
    1....................
    1.......................
    1..........................
    1.............................
    1...............................
    1.................................
    1...................................
    1..................................... and so on (it's sposed to be smooth)

    -I hope you get the idea of what I'm looking at
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    I might just guess the curve based on what it looks like...it sort of looks like a \frac{1}{x} curve
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  3. #3
    Junior Member
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    I'm going to think on this one...may get back to you. Thanks!
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  4. #4
    Eater of Worlds
    galactus's Avatar
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    Thanks
    1
    Yes, you can use your points to run a regression and then integrate the resulting expression/function you derive.

    Or, you can use data points and use Simpson's rule or another approximating method.

    Let's do an example:

    Suppose we want to build a road through a hill and have to move dirt. That's

    volume. The road is 75 feet wide and 600 feet long. We get the following horizontal distances(x) and heights(y) through the hill.

    x=0, 100, 200, 300, 400, 500, 600

    y=0,7,16,24,25,26,0

    We can run a quartic regression through a good calculator and derive the following equation

    f(x)=(9.09X10^{-10})x^{4}-(1.59X10^{-6})x^{3}+(5.93X10^{-4})x^{2}+.02x+.11

    75\int_{0}^{600}f(x)=673,707.60 \;\ ft^{2}

    Or, we can use simpson's rule without deriving an equation.

    V\approx{75}\cdot\frac{600}{18}\left[0+4(7)+2(16)+4(24)+2(25)+4(16)+0\right]=675,000 \;\ ft^{2}

    As you can see, they're both pretty close. The first would be the more accurate though, I would think, because R^2 = .998515

    Post some points and we'll derive the equation
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