MediumCalculusca-039

Arc Length Numeric

Problem

Approximate the arc length of y = f(x) over [a, b] with n straight segments, where f(x) = sum(coeffs[i] * x^i).

Sample n + 1 equally spaced points and sum sqrt(dx^2 + dy^2) over consecutive pairs. Return 0.0 when n <= 0.

Hint

A piecewise-linear approximation converges to the true arc length as n grows.

case 1

in: [[3],0,4,8]

expected: 4

case 2

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

expected: 6.708203932499369

case 3

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

expected: 4.6267234873447

case 4

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

expected: 1.4142135623730951

Starter codePython

def arc_length(coeffs, a, b, n):
    # Your code here
    pass

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