scipy.integrate.fixed_quad

scipy.integrate.fixed_quad(func, a, b, args=(), n=5)

Compute a definite integral using fixed-order Gaussian quadrature.

Integrate func from a to b using Gaussian quadrature of order n.

Parameters:

func : callable

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)).

a : float

Lower limit of integration.

b : float

Upper limit of integration.

args : tuple, optional

Extra arguments to pass to function, if any.

n : int, optional

Order of quadrature integration. Default is 5.

Returns:

val : float

Gaussian quadrature approximation to the integral

none : None

Statically returned value of None

See also

quad

adaptive quadrature using QUADPACK

dblquad

double integrals

tplquad

triple integrals

romberg

adaptive Romberg quadrature

quadrature

adaptive Gaussian quadrature

romb

integrators for sampled data

simps

integrators for sampled data

cumtrapz

cumulative integration for sampled data

ode

ODE integrator

odeint

ODE integrator

Examples

>>> from scipy import integrate
>>> 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