# scipy.integrate.quadrature

scipy.integrate.quadrature(func, a, b, args=(), tol=1.49e-08, rtol=1.49e-08, maxiter=50, vec_func=True, miniter=1)

  Compute a definite integral using fixed-tolerance Gaussian quadrature.

  Integrate func from a to b using Gaussian quadrature with absolute tolerance tol.

  Parameters:
    func function

      A Python function or method to integrate.

    a float

      Lower limit of integration.

    b float

      Upper limit of integration.

    args tuple, optional

      Extra arguments to pass to function.

    tol, rtol float, optional

      Iteration stops when error between last two iterates is less than tol OR the relative change is less than rtol.

    maxiter int, optional

      Maximum order of Gaussian quadrature.

    vec_func bool, optional

      True or False if func handles arrays as arguments (is a “vector” function). Default is True.

    miniter int, optional

      Minimum order of Gaussian quadrature.

  Returns:
    val float

      Gaussian quadrature approximation (within tolerance) to integral.

    err float

      Difference between last two estimates of the integral.

  See also

  `romberg`

    adaptive Romberg quadrature

  `fixed_quad`

    fixed-order Gaussian quadrature

  `quad`

    adaptive quadrature using QUADPACK

  `dblquad`

    double integrals

  `tplquad`

    triple integrals

  `romb`

    integrator for sampled data

  `simpson`

    integrator for sampled data

  `cumulative_trapezoid`

    cumulative integration for sampled data

  `ode`

    ODE integrator

  `odeint`

    ODE integrator

  Examples

      >>> from scipy import integrate
      >>> import numpy as np
      >>> f = lambda x: x**8
      >>> integrate.quadrature(f, 0.0, 1.0)
      (0.11111111111111106, 4.163336342344337e-17)
      >>> print(1/9.0)  # analytical result
      0.1111111111111111

      >>> integrate.quadrature(np.cos, 0.0, np.pi/2)
      (0.9999999999999536, 3.9611425250996035e-11)
      >>> np.sin(np.pi/2)-np.sin(0)  # analytical result
      1.0