### Riemann Sums Program code for the Sharp EL-9200 and EL-9300 calculators

Select NEW in the program menu. Then select REAL in the MODE menu. When prompted for a title, use "riemann". The "..." in the following program is where the integrand (the function to be integrated) should be entered.

`
`
Goto start

Label eqn

f=...

Return

Label start

Print "l-limit

Input a

Print "u-limit

Input b

Print "divns

Input n

x=a

s=0

i=1

h=(b-a)/n

Label 1

Gosub eqn

s=s+f*h

x=x+h

i=i+1

If i<=n Goto 1

Print "left sum

Print s

Gosub eqn

s=s+f*h

x=a

Gosub eqn

s=s-f*h

Print "right sum

Print s

End

**Comments on the program listing **
- Take care to distinguish between the character
`1` (one) and
the character `l` (lower case "ell"), and between `0` (zero) and `O` (upper case "oh").
- "Goto", "Label", Return", "Gosub", and "If" are in the BRANCH menu.
- "Print", the quote mark ", "Input", and "End" are in the PROG menu.
- = and <= are in the INEQ menu.

**Running the program**

- This program calculates left and right Riemann sums.
- The formula for the function to be integrated must be entered where the "..." appears above.
- The lower limit of integration must be less than the upper limit.
- As a test of the program, evaluate the definite integral of x^3 (x cubed) from A=1 to B=3 using
N=100 subdivisions. The left and right Riemann sums should be 19.7408 and 20.2608, respectively.

Back to the Math20A homepage.

*October 23, 1998*