## Simpson's rule for numerical integration

Version 1.5.0.0 (2.48 KB) by
The Simpson's rule uses parabolic arcs instead of the straight lines used in the trapezoidal rule
Updated 22 May 2013

Z = SIMPS(Y) computes an approximation of the integral of Y via the Simpson's method (with unit spacing). To compute the integral for spacing different from one, multiply Z by the spacing increment.

Z = SIMPS(X,Y) computes the integral of Y with respect to X using the Simpson's rule.

Z = SIMPS(X,Y,DIM) or SIMPS(Y,DIM) integrates across dimension DIM

SIMPS uses the same syntax as TRAPZ.

Example:
-------
% The integral of sin(x) on [0,pi] is 2
% Let us compare TRAPZ and SIMPS
x = linspace(0,pi,6);
y = sin(x);
trapz(x,y) % returns 1.9338
simps(x,y) % returns 2.0071

### Cite As

Damien Garcia (2024). Simpson's rule for numerical integration (https://www.mathworks.com/matlabcentral/fileexchange/25754-simpson-s-rule-for-numerical-integration), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2010a
Compatible with any release
##### Platform Compatibility
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Version Published Release Notes
1.5.0.0

Modification in the description

1.4.0.0

Modifications in the help text

1.2.0.0

Minor modifications in the descriptions and help texts of the two functions.