The Kitchin Research Group

we use the scipy.integrate.dblquad command

Integrate \(f(x,y)=y sin(x)+x cos(y)\) over

\(\pi <= x <= 2\pi\)

\(0 <= y <= \pi\)

i.e.

\(\int_{x=\pi}^{2\pi}\int_{y=0}^{\pi}y sin(x)+x cos(y)dydx\)

The syntax in dblquad is a bit more complicated than in Matlab. We have to provide callable functions for the range of the y-variable. Here they are constants, so we create lambda functions that return the constants. Also, note that the order of arguments in the integrand is different than in Matlab.

from scipy.integrate import dblquad
import numpy as np

def integrand(y, x):
    'y must be the first argument, and x the second.'
    return y * np.sin(x) + x * np.cos(y)

ans, err = dblquad(integrand, np.pi, 2*np.pi,
                   lambda x: 0,
                   lambda x: np.pi)
print ans

-9.86960440109

we use the tplquad command to integrate \(f(x,y,z)=y sin(x)+z cos(x)\) over the region

\(0 <= x <= \pi\)

\(0 <= y <= 1\)

\(-1 <= z <= 1\)

from scipy.integrate import tplquad
import numpy as np

def integrand(z, y, x):
    return y * np.sin(x) + z * np.cos(x)

ans, err = tplquad(integrand,
                   0, np.pi,  # x limits
                   lambda x: 0,
                   lambda x: 1, # y limits
                   lambda x,y: -1,
                   lambda x,y: 1) # z limits

print ans

2.0

scipy.integrate offers the same basic functionality as Matlab does. The syntax differs significantly for these simple examples, but the use of functions for the limits enables freedom to integrate over non-constant limits.