Casio fx-991CW: Arc of a Quadratic Curve
All screen shots will be taken with the https://www.classpad.app/ website.
Introduction
We are given three points: (x1, y1), (x2, y2), and (x3, y3) which are connected to a quadratic curve:
y(x) = a + b * x + c * x^2
with it’s derivative:
y’(x) = b + 2 * c * x
We assume that all three x-values are unique, therefore x1 ≠ x2, x2 ≠ x3, and x1 ≠ x3.
The arc length is the integral: ∫( √(1 + (b + 2 * c * x)^2 dx, min(x), max(x))
In curve fitting, if we only have three points, the quadratic curve will fit all three points.
Procedure
We can do the entire calculation in the Statistics app of the fx-991CW.
1. Go to the Statistics app by pressing [ Home ], selecting Statistics.
2. Enter the three points. If you need to, you can clear the lists by selecting Tools > Edit > Delete All.
3. Press [OK] (or [EXE] ), select Statistics Calc, y = a + b * x + c * x^2, and then press [OK] (or [EXE]) again. The Statistics Calc will allow us to make calculations using the statistics variables.
4. Calculate the integral:
∫ ( √(1 + (b + 2 * c * x)^2), min(x), max(x))
∫: Catalog > Func Analysis > Integration
b: Catalog > Statistics > Regression > b
c: Catalog > Statistics > Regression > c
min(x): Catalog > Statistics > Regression > Min/Max > min(x)
max(x): Catalog > Statistics > Regression > Min/Max > min(x)
Let’s walk through an example:
Points: (0,0), (5,4), (7,2)
Arc length: 9.97139451
You can see the procedure through the screen shots below:
Quadratic Curve:
Eddie
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