Integration Exercise 3

Imports



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%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
from scipy import integrate

2d polar integration

The 2d polar integral of a scalar function $f(r, \theta)$ is defined as:

$$ I(r_{max}) = \int_0^{r_{max}} \int_0^{2\pi} f(r, \theta) r d\theta $$

Write a function integrate_polar(f, rmax) that performs this integral numerically using scipy.integrate.dblquad.



In [13]:

    
def integrate_polar(f, rmax):
    """Integrate the function f(r, theta) over r=[0,rmax], theta=[0,2*np.pi]"""
    # YOUR CODE HERE
    d = lambda r, t: r * f(r, t)
    #Sarah helped me fix the bounds for r. 
    s = lambda y: 0.0
    l = lambda y: rmax
    h, e = integrate.dblquad(d, 0.0, 2*np.pi, s, l)
    return h



In [14]:

    
assert np.allclose(integrate_polar(lambda r,t: 1, 1.0), np.pi)
assert np.allclose(integrate_polar(lambda r, t: np.exp(-r)*(np.cos(t)**2), np.inf), np.pi)



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