MediumCalculusca-303

Leibniz Rule Moving Limits

Problem

When both integration limits depend on x, d/dx of the integral from a(x) to b(x) of f(t) dt = f(b(x)) * b'(x) - f(a(x)) * a'(x).

Given coefficients of the polynomial integrand f, coefficients of the linear limits a and b, and x, return the derivative value. Coeffs lists are in ascending order.

Hint

Evaluate the integrand at each moving endpoint, then multiply by that endpoint's derivative.

Test cases

case 1

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

expected: -1

case 2

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

expected: 2

case 3

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

expected: -6

Starter codePython

def leibniz_rule_value(f_coeffs, a_coeffs, b_coeffs, x):
    # Your code here
    pass

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