3. Construct a quadrature rule of the form [ƒ(x)da ≈ A₁f (−1) + A₁f(0) + A₂ƒ(1), which is exact for polynomials of degree <2. (a) Derive the 3-point (Legendre) Gaussian quadrature to approximate f₁₁ f(x)dx (i.e. you need to obtain the nodes 20, 1, 2 and the corresponding weights 40, A1, A2). (b) Verify its degree of precision. (c) Compare the accuracy of this 3-point Gaussian quadrature with that of the elementary Simpson rule for approximating ₁₁e²dx. *All course materials (class lectures and discussions, handouts, homework assignments, examinations, web ma- terials) and the intellectual content of the course itself are protected by United States Federal Copyright Law, the California Civil Code. The UC Policy 102.23 expressly prohibits students (and all other persons) from recording lectures or discussions and from distributing or selling lectures notes and all other course materials without the prior written permission of Prof. Hector D. Ceniceros. 1 (d) Show that the 3-point Gaussian quadrature can be used for approximating for f(x)dx by doing a simple change of variables and apply this to approximate S sin x x dx.