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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