**HP Prime and TI-84 Plus CE: Simpson’s Rule**

Caption: The Simpson’s
Rule applied on ∫ X^2*e^X dx from X = 1 to 4

Actual value:
543.2632185

The program SIMPRULE approximates the integral of f(X)

∫ f(X) dX = h/3 * ( f(a) + 2*Σf(x_E) + 4*∑f(x_O) + f(b) )

Where:

a = the lower limit

b = the upper limit

n = the number of intervals,

**n is even**
h = (b – a)/n

x_E = a + h*I where I is from 1 to n-1 and I is even

x_O = a + h*I where I is from 1 to n-1 and I is odd

**HP Prime Program: SIMPRULE**

EXPORT SIMPRULE()

BEGIN

//
EWS 2016-06-05

HAngle:=0;
// Radians

LOCAL
f;

INPUT({{f,[8]},A,B,N},

"Simpson
Rule",

{"f(X)=","Low:","High:",

"Intervals
(Even):"});

H:=(B-A)/N;

X:=A;
T:=EVAL(f);

X:=B;
T:=EVAL(f)+T;

FOR
I FROM 1 TO N-1 DO

X:=A+I*H;

IF
FP(I/2)==0 THEN

T:=2*EVAL(f)+T;

ELSE

T:=4*EVAL(f)+T;

END;

END;

T:=T*H/3;

RETURN
T;

END;

**TI-84 Plus CE Program: SIMPRULE**

Radian:Func

Input "LOW:",A

Input "HIGH:",B

Input "N (EVEN):",N

(B-A)/N→H

A→X:Y₁→T

B→X:Y₁+T→T

For(I,1,N-1)

A+I*H→X

If fPart(I/2)=0

Then

2*Y₁+T→T

Else

4*Y₁+T→T

End

End

T*H/3→T

Disp "INTEGRAL=",T

**Examples:**

Example 1:

∫ cos^2 X dX from X = 0 to X = π, n = 14

Approximation:
1.570796327

Example 2:

∫ X^2 + 3*X – 6 dX from X = 1 to X = 3, n = 14

Approximation: 8.66666667

Eddie

**Source:**

Burden, Richard L. and Faires, J. Douglas. “Numerical Analysis” 8

^{th}Ed. Thompson Brooks/Cole: Belmont, CA. 2005
This blog is property of Edward Shore, 2016.

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