MediumCalculusca-304

Numerical Arc Length of a Polynomial

Problem

Approximate the arc length of y = f(x) on [a, b] with the midpoint sum of sqrt(1 + f'(x)^2) * dx over n equal subintervals.

Given polynomial coefficients, a, b, and n, return the estimate.

Hint

Integrate the speed sqrt(1 + (f')^2); a flat line gives the plain distance.

case 1

in: [[0,0,1],0,1,100]

expected: 1.4789354039742377

case 2

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

expected: 2.8284271247461903

case 3

in: [[0,0,0],0,1,10]

expected: 1

Starter codePython

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

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