(a) Show that the polynomials p1(x) = 1, p2(x) - 1/2 - p3(x) = x2 - x...

Question:

(a) Show that the polynomials p1(x) = 1, p2(x) - 1/2 - p3(x) = x2 - x + 1/6 are mutually orthogonal with respect to the L2 inner product on the interval [0, 1 ].
(b) Show that the functions sin n π x, n = 1, 2, 3, .... are mutually orthogonal with respect to the same inner product.