Produces the integral at each input point on curve C. The curve is presented to this function as two arrays containing the ordinal and abscissal components of the curve. To compute the integral at each point, INTEGR fits a cubic spline to the curve and returns the integrals of the approximating polynomials at each point. The curve of integrals that INTEGR returns has the same number of values as each of the arguments.
The algorithm that fits the cubic spline is from Computer Methods for Mathematical Computations by Forsythe, Malcolm and Moler (1977, Prentice-Hall: Englewood Cliffs, NJ). The
CSPLINE function uses the same algorithm.
Format
INTEGR (Independent Points, Dependent Points)
Arguments
Independent Points | The X or ordinal values of the curve to be integrated. |
Dependent Points | The Y or abscissal values of the curve to be integrated. |
Example
The following example illustrates the use of the INTEGR function:
Function | INTEGR(SERIES(0,1,5), {0,1,4,9,16}) |
Result | 0.0, 0.333, 2.667, 9.0, 21.333 |