Show that the shifted Gauss–Legendre rule computed in qgaustb actually will integrate polynomials of degree 5 exactly by trying p(x) = 30x5 +20x4 +12x3 +6x2 +2x +1. Construct a linear tranformation...

Show that the shifted Gauss–Legendre rule computed in qgaustb actually will integrate polynomials of degree 5 exactly by trying p(x) = 30x5 +20x4 +12x3 +6x2 +2x +1.

Construct a linear tranformation that takes the fundamental triangle with vertices at (0, 0), (1, 0), and (0,1) to the triangle with vertices at (a1, b1), (a2, b2), and (a3, b3).