Casio Prizm Color Programs
This blog will feature two
programs: arc length and area between
curves. After the calculation is
complete, the results are displayed and plotted.
ARCPRZ:
Arc Length
Find the Arc Length of function Y1.
Once the arc length is calculated, the function is plotted, and the arc length
is plotted in red.
Notes:
* Functions are retrieved by
pressing [VARS], [ F4 ] (GRAPH), [ F1 ] ( Y
).
* To get Xdot, press [ VARS ], [ F1 ] (V-WIN), [ F1 ] ( X ), [ F4 ] for
Xdot.
* Color commands are found by
pressing [SHIFT] [ 5 ] (FORMAT) and selecting Color commands.
* The derivative function (d/dx)
is not allowed as part of the integrand in the integral function (∫ dx) on Casio
calculators. (At least for the fx-5800p, fx-9750g series, fx-9860g series, and the
Prizm. I am not sure about the
Classpads). Therefore, the Simpson’s
Rule is used instead. I use 100
divisions.
* G SelOn and G SelOff I got from
the CATALOG. ([SHIFT], [ 4 ]). I am not sure what menus where these two
commands are located.
* DrawGraph is found by pressing
[SHIFT] [ VARS ] (PRGM), [ F6 ] (next page), [ F2 ] (DISPLAY), [ F2 ] (Graph)
Program:
Rad
Menu
"USE Y1?","YES",1,"NO",2
Lbl
2
"Y1 (NO QUOTES)"? → Y1
Lbl
1
"LOW"?
→ A
"HIGH"?
→ B
0→K:(B-A)÷100→S
0→T
For
A→I To B Step S
√
(1+d/dx(Y1,I)^2)→U
I=A
Or I=B ⇒ T+U → T
If
K≠0 And K≠100
Then
2U+T
→ T
Frac
(K/2)≠0 =>2U+T → T
IfEnd
K+1
→ K
Next
S/3*T
→ T
"ARC
LENGTH=" ◢
T ◢
G
SelOff
G
SelOn 1
DrawGraph
For
A → I To B Step Xdot
Red
PlotOn I, Y1(I)
Next
Black
Text 165,1,"ARC="
Black
Text 165,65,T
Examples
Y1 = cos(X)*e^X from X = 1 to 2. Arc Length =
4.7031139029…
Y1 = -2X^2 + 4X + 1 rom X = -2 to 2. Arc Length =
20.7833…
AREABTWN: Area Between
Curves
This calculates the area
between two curves, Y1 and Y2. This program works best if
you can set the graph screen to where the curves intersect at only two
points. The program first searches for two intersections, one from the
left side of the graph screen (Xmin) and one from the right (Xmax). After
the area is calculated, both curves are graphed and the area between curves are
shaded. Function and Radian modes are used.
Notes:
* F-Line is found by
pressing [SHIFT] [ F4 ] (Sketch), [ F6 ] (next page)
* Since there is no shade function on the Prizm,
a work around is needed. Thankfully,
there are FMin and FMax (function minimum and function maximum) functions that
would make the picture look nice possible.
* ViewWindow seems to only
affect the graph shown in Program mode when used as a command in program made.
* The program assumes that
Function mode is set.
* In this listing,
anything followed by double slashes (//) is a comment. Do not type these lines into the
program.
Program:
Rad
Menu
“USE Y1, Y2?”, “YES”, 1, “NO”, 2
Lbl
2
“Y1 (NO QUOTES)”? → Y1
“Y2 (NO QUOTES)”? → Y2
Lbl
1
//
finding the end points
Solve(Y1-Y2,
Xmin) → A
Sovle(Y1-Y2,
Xmax) → B
If
A > B
Then
A
→ C: B → A: C → B: IfEnd
If
A = B
Then
“NO
SOLUTION”
Stop:
IfEnd
//
calculation
∫
(Y1-Y2, A, B) → I
Abs
I → I
“AREA=”
◢
I ◢
// start graphing routine
ClrGraph
G SelOff
G SelOn 1
G SelOn 2
// setting the window
FMin(Y1,
A, B) → List 25
FMin(Y2,
A, B) → List 26
List 25[2] → U
List 26[2] → V
Min({U,V}) → E
FMax(Y1,
A, B) → List 25
FMax(Y2,
A, B) → List 26
List 25[2] → U
List 26[2] → V
Max({U,V}) → F
ViewWindow A-1,B+1,1,E-1,F+1,1
// now draw the graph
DrawGraph
// shading routine
For A → K To B Step Xdot
Green F-Line K, Y1(K),K,Y2(K)
Next
Examples
The Standard Window is used. Xmin = -10, Xmax = 10, Ymin =
-10, Ymax = 10
Y1 = -2X^2 + 4X + 1, Y2 =
X^2. Area = 2.734721…
Y1 = 1.2X + .63, Y2 = -X^2 + 5X + 1. Area =
10.58676675…
A nice feature of the Prizm is that you transfer program
files and screen captures from the calculator to the computer by just using the
standard mini USB cable.
Eddie