The RSUM program calculates the left-hand, right-hand, trapezoidal, midpoint and SimpsonRiemann sums to estimate the value of a single integral of any reasonably well-behaved real-valued function. For example,

.

The *x _{i}* sample values are evenly spaced, with separation . Of course,both the sample values and the weights

On entry, RSUM expects the following information on the stack:

level 5: Integrand

level 4: Independent variable (that is used in level 5)

level 3: Lower limit of integration

level 2: Upper limit of integration

level 1: Number of subdivisions

For example, to approximate by using 15 subdivisions, we would enter the following:

level 5: 'LOG(1+T)/T'

level 4: 'T'

level 3: 1

level 2: 100

level 1: 15

After running RSUM, the stack display on the right would appear.

Scrolling up the stack (by using the up-arrow key), we would also discover: