DADiSP Worksheet Functions > Function Categories > Statistics and Calculus > CUMTRAPZ
Calculates the integral of a series using the trapezoidal rule.
CUMTRAPZ(series)
series |
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An interval or XY series, the input. |
CUMTRAPZ(xseries, yseries)
xseries |
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A series, the X values. |
yseries |
- |
A series, the Y values. |
A series.
W1: {0, 2, 4, 6, 8, 10}
W2: integ(W1)
W3: cumtrapz(W1)
W2 == {0.0, 1.3, 4.0, 9.3, 16.0, 25.3}
W3 == {0.0, 1.0, 4.0, 9.0, 16.0, 25.0}
W2 contains the integrated series using Simpson's rule.
W3 contains the integrated series using the Trapezoidal rule.
y1 = gnorm(1000, .001);
a1 = cumtrapz(y1);
a2 = trapz(y1);
Series a1 contains the cumulative area of y1 and scalar a2 contains the value of the total area of y1. Note that a1[end] == a2, the last point of the cumulative area equals the total area.
The trapezoidal rule fits a line between two data points and calculates the area under the resulting trapezoid such that:
where
For an interval series s, the trapezoidal rule calculates the running sum:
See TRAPZ to compute the total area using the trapezoidal rule.
See INTEG to compute the cumulative area using Simpson’s rule.