Question: The Laguerre polynomials L0(x) = 1, L1(x) = 1 x, L2(x) = x2 4x + 2, and L3(x) = x3 + 9x2

The Laguerre polynomials L0(x) = 1, L1(x) = 1 ˆ’ x, L2(x) = x2 ˆ’ 4x + 2, and L3(x) = ˆ’x3 + 9x2 ˆ’ 18x + 6 are derived in Exercise 11 of Section 8.2. As shown in Exercise 6, these polynomials are useful in approximating integrals of the form

a. Derive the quadrature formula using n = 2 and the zeros of L2(x).
b. Derive the quadrature formula using n = 3 and the zeros of L3(x).

c" f (x) dx = 0.

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