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scipy.integrate.newton_cotes¶
- scipy.integrate.newton_cotes(rn, equal=0)[source]¶
Return weights and error coefficient for Newton-Cotes integration.
Suppose we have (N+1) samples of f at the positions x_0, x_1, ..., x_N. Then an N-point Newton-Cotes formula for the integral between x_0 and x_N is:
∫xNx0f(x)dx=Δx∑Ni=0aif(xi)+BN(Δx)N+2fN+1(ξ)
where ξ∈[x0,xN] and Δx=xN−x0N is the average samples spacing.
If the samples are equally-spaced and N is even, then the error term is BN(Δx)N+3fN+2(ξ).
Parameters: rn : int
The integer order for equally-spaced data or the relative positions of the samples with the first sample at 0 and the last at N, where N+1 is the length of rn. N is the order of the Newton-Cotes integration.
equal : int, optional
Set to 1 to enforce equally spaced data.
Returns: an : ndarray
1-D array of weights to apply to the function at the provided sample positions.
B : float
Error coefficient.
Notes
Normally, the Newton-Cotes rules are used on smaller integration regions and a composite rule is used to return the total integral.