# scipy.integrate.simps¶

scipy.integrate.simps(y, x=None, dx=1, axis=-1, even='avg')[source]

Integrate y(x) using samples along the given axis and the composite Simpson’s rule. If x is None, spacing of dx is assumed.

If there are an even number of samples, N, then there are an odd number of intervals (N-1), but Simpson’s rule requires an even number of intervals. The parameter ‘even’ controls how this is handled.

Parameters: y : array_like Array to be integrated. x : array_like, optional If given, the points at which y is sampled. dx : int, optional Spacing of integration points along axis of y. Only used when x is None. Default is 1. axis : int, optional Axis along which to integrate. Default is the last axis. even : str {‘avg’, ‘first’, ‘last’}, optional ‘avg’ : Average two results:1) use the first N-2 intervals with a trapezoidal rule on the last interval and 2) use the last N-2 intervals with a trapezoidal rule on the first interval. ‘first’ : Use Simpson’s rule for the first N-2 intervals with a trapezoidal rule on the last interval. ‘last’ : Use Simpson’s rule for the last N-2 intervals with a trapezoidal rule on the first interval.

quad
romberg
quadrature
fixed_quad
dblquad
double integrals
tplquad
triple integrals
romb
integrators for sampled data
cumtrapz
cumulative integration for sampled data
ode
ODE integrators
odeint
ODE integrators

Notes

For an odd number of samples that are equally spaced the result is exact if the function is a polynomial of order 3 or less. If the samples are not equally spaced, then the result is exact only if the function is a polynomial of order 2 or less.