Exercise: double integral with Gauss-Legendre

Compute ∫_{1.4}^{2}∫_{1}^{1.5} ln(x+2y) dy dx with Gauss-Legendre and n=m=3.

1. The changes of variables are:

   $$x=0.3u+1.7,\qquad y=0.25v+1.25$$

2. The product of Jacobians is $0.3\cdot 0.25=0.075$:

   $$I=0.075\int_{-1}^{1}\int_{-1}^{1}\ln(0.3u+0.5v+4.2)\,dv\,du$$

3. With nodes 0, ±0.774597 and weights 0.888889, 0.555556, 0.555556:

   $$I\approx0.075\sum_{i=1}^{3}\sum_{j=1}^{3}c_i c_j\ln(0.3u_i+0.5v_j+4.2)$$