scipy.integrate.dblquad(func, a, b, gfun, hfun, args=(), epsabs=1.49e-08, epsrel=1.49e-08)

Compute a double integral.

Return the double (definite) integral of func(y,x) from x=a..b and y=gfun(x)..hfun(x).

Parameters :

func : callable

A Python function or method of at least two variables: y must be the first argument and x the second argument.

(a,b) : tuple

The limits of integration in x: a < b

gfun : callable

The lower boundary curve in y which is a function taking a single floating point argument (x) and returning a floating point result: a lambda function can be useful here.

hfun : callable

The upper boundary curve in y (same requirements as gfun).

args : sequence, optional

Extra arguments to pass to func2d.

epsabs : float, optional

Absolute tolerance passed directly to the inner 1-D quadrature integration. Default is 1.49e-8.

epsrel : float

Relative tolerance of the inner 1-D integrals. Default is 1.49e-8.

Returns :

y : float

The resultant integral.

abserr : float

An estimate of the error.

See also

single integral
triple integral
fixed-order Gaussian quadrature
adaptive Gaussian quadrature

odeint, ode, simps, trapz, romb

for coefficients and roots of orthogonal polynomials

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