SciPy

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:
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

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