TI-84 Plus and Casio Prizm: Area between Polynomials p(x) and q(x)

TI-84 Plus and Casio Prizm:  Area between Polynomials p(x) and q(x)

The program POLYSURF calculates the area of a surfaces with:

* Side borders are straight vertical lines.  The left border line begins at x = 0

* The top and the bottom are defined polynomials: p(x) for the top and q(x) for the bottom.

* There are n partitions in the shape, for all partition points, p(x) > q(x).

The program also draws the shape.  If the number of partitions are 4 or less, an exact area is calculated.  Otherwise, p(x) and q(x) are approximated by a quartic polynomial and an approximated area is calculated.

TI-84 Plus Program POLYSURF

"EWS 2016-12-06"

Disp "P(X) > Q(X)"

FnOff

PlotsOff

{0}→L₁

Input "P(0)=",P

{P}→L₂

Input "Q(0)=",Q

{Q}→L₃

Input "NO. OF PARTITIONS:",N

For(I,1,N)

ClrHome

Output(7,1,"POINT")

Output(7,8,I)

Output(8,1,"P(X)>Q(X)")

Input "X:",X

Input "P(X):",P

Input "Q(X):",Q

augment(L₁,{X})→L₁

augment(L₂,{P})→L₂

augment(L₃,{Q})→L₃

End

L₁(dim(L₁))→L

If N=1

Then

LinReg(ax+b) L₁,L₂,Y₁

LinReg(ax+b) L₁,L₃,Y₂

End

If N=2

Then

QuadReg L₁,L₂,Y₁

QuadReg L₁,L₃,Y₂

End

If N=3

Then

CubicReg L₁,L₂,Y₁

CubicReg L₁,L₃,Y₂

End

If N≥4

Then

QuartReg L₁,L₂,Y₁

QuartReg L₁,L₃,Y₂

End

FnOn 1,2

fnInt(Y₁-Y₂,X,0,L)→S

Disp "AREA=",S

Pause

ClrDraw

­.5→Xmin

L+.5→Xmax

min(L₃)-.5→Ymin

max(L₂)+.5→Ymax

Shade(Y₂,Y₁,0,L)

Casio Prizm Program:  POLYSURF

The character # can be found by exiting to the “main” program menu (TOP, BOTTOM, etc).  Press F6 for CHAR, select #, and press [EXE].

Get the regressions by pressing [F4] (MENU), [F1] (STAT), [F6] twice (CALC, >) and selecting the regression.  The statistic variables a, b, c, d, and e are calculated after regression calculation.

“EWS 2016-12-06”

“P(x)>Q(x)”

{0} → List 1

“P(0)=”? → P

{P} → List 2

“Q(0)=”? → Q

{Q} → List 3

“# PARTITIONS:”? → N

For 1 → I To N

“POINT”

I ◢

“X:”? → X

“P(X):”? → P

“Q(X):”? → Q

Augment(List 1, {X}) → List 1

Augment(List 2, {P}) → List 2

Augment(List 3, {Q}) → List 3

Next

If N = 1

Then

LinearReg (ax+b) List 1, List 2

a → A

b → B

“Ax+B” → Y1

LinearReg (ax+b) List 1, List 3

a → F

b → G

“Fx+G” → Y2

IfEnd

If N = 2

Then

QuadReg List 1, List 2

a → A

b → B

c → C

“Ax^2+Bx+C” → Y1

QuadReg List 1, List 3

a → F

b → G

c → H

“Fx^2+Gx+H” → Y2

IfEnd

If N = 3

Then

CubicReg List 1, List 2

a → A

b → B

c → C

d → D

“Ax^3+Bx^2+Cx+D” → Y1

CubicReg List 1, List 3

a → F

b → G

c → H

d → I

“Fx^3+Gx^2+Hx+I” → Y2

IfEnd

If N ≥ 4

Then

QuartReg List 1, List 2

a → A

b → B

c → C

d → D

e → E

“Ax^4+Bx^3+Cx^2+Dx+E” → Y1

CubicReg List 1, List 3

a → F

b → G

c → H

d → I

e → J

“Fx^4+Gx^3+Hx^2+Ix+J” → Y2

IfEnd

List 1[Dim List 1] → L

∫(Y1-Y2, 0, L) → S

“AREA=”

S ◢

ClrGraph

ViewWindow -.5, L+.5, 1, Min(List 3)-.5, Max(List 2)+.5, 1

F-Line 0, List 2[1], 0, List 1[3]

Dim List 1 → Z

F-line List 1[Z], List 2[Z], List 1[Z], List 3[Z]

DrawGraph

Examples

Example 1

Data:

n	x	p(x)	q(x)
0	0	2	-2
1	1	5	-2
2	2	2	-2

Number of partitions, n = 2

Area = 12

Example 2

Data:

n	x	p(x)	q(x)
0	0.0	0.00	0.00
1	1.5	5.62	-0.64
2	2.5	3.83	1.38
3	3.5	1.25	0.76

Number of Partitions, n = 3

Area ≈ 13.16619792

Example 3

Data:

n	x	p(x)	q(x)
0	0.00	3.00	-3.00
1	0.50	2.54	-2.84
2	1.25	2.01	-3.00
3	1.60	2.36	-3.55
4	2.00	2.76	-1.98

Number of Partitions, n = 4

 Area ≈ 10.77281698

This blog is property of Edward Shore, 2016