(30b) Numerical Integration

[Dwight Sturrock]

This program will evaluate a formula stored in subroutine 99 for the definite integral using the Trapezoidal rule.

EXAMPLE
1. Enter the main program listed below
2. Enter a formula into subroutine 99. A routine to evaluate the formula sin(x)/ln(x) would look like this:

Lbl 99
Input
Sin
Swap
Ln
/
RTN

3. Enter the lower, then the upper limit of integration. To evaluate sin(x)/ln(x) at the limits 1.2 and 10 (lower limit 1st):

1.2
Input
10
Input

4. Run the program- shift key+ Prgm, use the up/down arrow keys to select the proper program, and press =

It takes about 15 seconds to calculate simple integrals. Accuracy can be increased as noted below, but calculation time will also increase.

   

MAIN PROGRAM LISTING (comments start with //):
Intergrat //enter this using the MSG command
STO 1 //store the lower and higher limits of integration
Swap
STO 2

- //the span (low, high) is divided up by the number of partitions
1
EEX
3 //1000 partitions. Increasing # of partitions will increase accuracy
/
STO 2

0
STO 5 //zero out storage register 5

RCL 0
Call 99 //evaluate the function at X1
STO 3 //result= XY1
Lbl 50
RCL 0
RCL 2 //h increment
+
STO 0 //next X1
Call 99 //evaluate function at X2
STO 4 //XY2
RCL 3 //XY1
+ //take the average
2
/
RCL 2 //calculate the area
*
STO +5 //add to area

RCL 4 //XY2 becomes-
STO 3 //XY1

RCL 0 //reached upper limit?
RCL 1
?<
GT50
RCL 5 //display definite integral
Stop