MediumCalculusca-168

Polar Area Integral

Problem

Evaluate the polar integral of x^2 + y^2 over the disk of radius R.

The change to polar coordinates with Jacobian r gives the integral of r^3 dr dtheta, which equals pi * R^4 / 2. Given R >= 0, return this value using 3.141592653589793 for pi.

Hint

The integrand becomes r^2 and the area element becomes r dr dtheta.

Test cases

case 1

in: [1]

expected: 1.5707963267948966

case 2

in: [2]

expected: 25.132741228718345

case 3

in: [0]

expected: 0

case 4

in: [0.5]

expected: 0.09817477042468103

Starter codePython

def polar_moment(radius):
    # Your code here
    pass

4 test cases · run your code against them in the editor