MediumCalculusca-159

Surface Integral over Plane

Problem

Integrate z = a - b*x - c*y over the triangle T with vertices (0,0), (1,0), (0,1).

Using the triangle's centroid (1/3, 1/3) the integral is a/2 - b/6 - c/6. Given a, b, c, return the value of this integral.

Hint

The average of a linear function over a triangle is its value at the centroid.

case 1

in: [1,1,1]

expected: 0.1666666666666667

case 2

in: [6,0,0]

expected: 3

case 3

in: [0,1,0]

expected: -0.16666666666666666

case 4

in: [2,3,3]

expected: 0

Starter codePython

def surface_integral_plane(a, b, c):
    # Your code here
    pass

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