MediumCalculusca-259

Scalar Line Integral on a Segment

Problem

The scalar line integral of f(x, y) = alpha*x + beta*y + gamma along the straight segment from P to Q integrates f with respect to arc length.

Because f is linear along the segment, the integral equals length(P, Q) * (f(P) + f(Q)) / 2. Given the coefficients and the endpoints as [x, y] pairs, return the integral.

Hint

The trapezoid rule is exact when the integrand is linear in the parameter.

Test cases

case 1

in: [1,0,0,[0,0],[3,4]]

expected: 7.5

case 2

in: [0,0,1,[0,0],[3,4]]

expected: 5

case 3

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

expected: 1.4142135623730951

case 4

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

expected: 0

Starter codePython

def scalar_line_integral(alpha, beta, gamma, p, q):
    # Your code here
    pass

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