Syntax: |
vout = INTEGRAL(x,y)
|
The INTEGRAL
function integrates the vector
y
, the dependent variable, with respect to
vector x
, the independent variable.
The output of this function is a vector with the same length as x
. The last
element of the output vector is the integral over the full
range of x
. Currently, integration using
interpolating splines, using no keyword or the keyword SMOOTH
,
or the trapezoid rule, using keyword TRAPEZOID
, are the only types available.
Interpolating splines
Syntax: | vout = INTEGRAL(x,y)
|
This integration method utilizes an interpolating spline under tension. The spline tension
used is the current value of
TENSION
, which may be
changed with the SET TENSION
command. The nature of the interpolating curve varies continuously from pure cubic
splines, for TENSION = 0
, to a piecewise linear curve, that is,
points joined by straight line segments, for large TENSION
.
x
must be strictly monotonically increasing.
Example
The following code produces the picture below (except for the text which was added interactively).
clear
defaults
!
pi=acos(-1)
generate x 0,,2*pi 100
y = cos(x)^3+sin(x)^3
graph x y
!
set linecolor red
graph/overlay x integral(x,y)
set linecolor black
replot
Trapezoid rule
Syntax: vout = INTEGRAL(x,y,'TRAPEZOID')
This integration method uses the trapezoid rule.