MediumCalculusca-305

Surface Area of Revolution Numeric

Problem

The surface area of the solid formed by rotating y = f(x) about the x-axis is the integral of 2 * pi * f(x) * sqrt(1 + f'(x)^2) dx.

Approximate it with the midpoint rule over n equal subintervals. Given polynomial coefficients, a, b, and n, return the estimate.

Hint

The integrand is circumference 2*pi*f(x) times the arc-length factor.

case 1

in: [[0,1],0,2,50]

expected: 17.771531752633464

case 2

in: [[1],0,3,6]

expected: 18.84955592153876

case 3

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

expected: 0

Starter codePython

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

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