Question: 6. Let {lo(x), l1(x), (2(x), . .., In(x)} be the orthogonal set of Legendre polynomials over the interval (0, 1). The average value of a

6. Let {lo(x), l1(x), (2(x), . .., In(x)} be the orthogonal

6. Let {lo(x), l1(x), (2(x), . .., In(x)} be the orthogonal set of Legendre polynomials over the interval (0, 1). The average value of a function f, over the interval (0, 1), is defined as ( f(x) da. Prove that the average value of a Legendre polynomial (;(x) is 0 if j 2 1

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