Casio fx-CG 50: Centroid of a 2D spaces
The program CENTROID calculates the center point for an area covered by:
y(x) ≥ 0, x ≥ lower limit, x ≤ upper limit
The center point is calculated by:
x-center = ∫( x * y(x) dx, x = lower limit, x = upper limit) / A
y-center = ∫(1 / 2 * y(x)^2 dx, x = lower limit, x = upper limit) / A
where A = ∫( y(x) dx, x = lower limit, x = upper limit)
Casio fx-CG 50 Program Code: CENTROID
Here is the code, which includes a graphic representation of y(x) and the location of the centroid. In this code, the Y is bold and it comes from the VARS menu. Do not merely use ALPHA+Y. For calculators with monochrome screens, such as the fx-9750G/fx-9860G series, leave out the color commands (Black, Blue, Red). The program assumes that there no preset plots or more than one function to be plotted.
This program works best for functions y(x) ≥ 0 for x ∈ [lower limit, upper limit].
Here is a text-only version:
Examples
Example 1: y = x^2 , lower limit = 0, upper limit = 1
X-Center = 3 / 4 = 0.75
Y-Center = 3 / 10 = 0.3
Example 2: y = 2 * cos( x / 2 ), lower limit = 0, upper limit = π
X-Center ≈ 1.141592654
Y-Center ≈ 0.7853981634
Example 3: y = 3, lower limit = 1, upper limit = 5
X-Center = 3
Y-Center = 1.5
Example 4: y = -4 * x^2 + 2 * x + 6, lower limit = -0.5, upper limit = 1
X-Center = 1 / 4
Y-Center = 307 / 110
Eddie
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