EasyCalculusca-096

Gauss-Legendre 2-Point Integration

Problem

Approximate the integral of f(x) = sum(coeffs[i] * x^i) over [a, b] with the 2-point Gauss-Legendre rule:

integral ≈ (b - a)/2 * (f(m - d) + f(m + d))

where m = (a + b)/2 and d = (b - a)/(2*sqrt(3)). The rule is exact for polynomials up to degree 3.

Hint

Shift the standard nodes ±1/sqrt(3) from [-1, 1] onto the interval [a, b].

case 1

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

expected: 2.6666666666666665

case 2

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

expected: 0

case 3

in: [[1],0,5]

expected: 5

case 4

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

expected: 8

case 5

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

expected: 0.22222222222222235

Starter codePython

def gauss_legendre_2(coeffs, a, b):
    # Your code here
    pass

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