scipy.integrate.
fixed_quad#
- scipy.integrate.fixed_quad(func, a, b, args=(), n=5)[source]#
Compute a definite integral using fixed-order Gaussian quadrature.
Integrate func from a to b using Gaussian quadrature of order n.
- Parameters:
- funccallable
A Python function or method to integrate (must accept vector inputs). If integrating a vector-valued function, the returned array must have shape
(..., len(x))
.- afloat
Lower limit of integration.
- bfloat
Upper limit of integration.
- argstuple, optional
Extra arguments to pass to function, if any.
- nint, optional
Order of quadrature integration. Default is 5.
- Returns:
- valfloat
Gaussian quadrature approximation to the integral
- noneNone
Statically returned value of None
See also
Examples
>>> from scipy import integrate >>> import numpy as np >>> f = lambda x: x**8 >>> integrate.fixed_quad(f, 0.0, 1.0, n=4) (0.1110884353741496, None) >>> integrate.fixed_quad(f, 0.0, 1.0, n=5) (0.11111111111111102, None) >>> print(1/9.0) # analytical result 0.1111111111111111
>>> integrate.fixed_quad(np.cos, 0.0, np.pi/2, n=4) (0.9999999771971152, None) >>> integrate.fixed_quad(np.cos, 0.0, np.pi/2, n=5) (1.000000000039565, None) >>> np.sin(np.pi/2)-np.sin(0) # analytical result 1.0