MediumCalculusca-299

Gauss-Legendre 2-Point on Interval

Problem

Map two-point Gauss-Legendre to a general interval [a, b]: nodes are c +/- (b - a) / (2 * sqrt(3)) with c = (a + b) / 2, and each weight is (b - a) / 2.

Given polynomial coefficients and the interval bounds, return the quadrature estimate.

Hint

Affine-map the standard nodes and scale the weights by half the interval length.

Test cases

case 1

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

expected: 0.3333333333333333

case 2

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

expected: 2

case 3

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

expected: 7.999999999999999

Starter codePython

def gauss_legendre_2_interval(coeffs, a, b):
    # Your code here
    pass

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