Line Integral on a Segment

Problem

Compute the line integral of the linear field F(x, y) = [a*x + b*y, c*x + d*y] along the straight segment from P = (x0, y0) to Q = (x1, y1).

Parameterize r(t) = P + t*(Q - P) for t in [0, 1]. Because F is linear, the integrand F(r(t)) · (Q - P) is linear in t, so the integral equals the average of its endpoint values.

Hint

The average of the integrand at the two endpoints is exact when the integrand is linear in t.

Test cases

case 1

in: [1,0,0,1,0,0,2,3]

expected: 6.5

case 2

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

expected: 1

case 3

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

expected: 0

case 4

in: [1,0,0,0,1,1,4,5]

expected: 7.5

Starter codePython

def line_integral(a, b, c, d, x0, y0, x1, y1):
    # Your code here
    pass

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