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