MediumCalculusca-077

Divergence Theorem Check

Problem

The divergence theorem says the outward flux of F across a closed surface equals the integral of div F over the enclosed region.

For F(x, y) = [a*x + b*y, c*x + d*y] and the rectangle [0, w] x [0, h], the divergence is the constant a + d, so the flux is (a + d) * w * h.

Hint

Integrate the constant divergence over the area of the rectangle.

case 1

in: [1,0,0,1,1,1]

expected: 2

case 2

in: [2,5,-3,1,3,2]

expected: 18

case 3

in: [0,0,0,0,5,5]

expected: 0

case 4

in: [-1,0,0,1,2,4]

expected: 0

Starter codePython

def divergence_theorem_check(a, b, c, d, w, h):
    # Return the flux through the rectangle boundary
    # Your code here
    pass

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