Derive the local Three-point Gauss Quadrature Formula for integrating a function f(x) over the reference interval...

 

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Derive the local Three-point Gauss Quadrature Formula for integrating a function f(x) over the reference interval [-1, 1]. (This formula uses the roots of the orthogonal polynomial 3(x).) Use the corresponding composite formula to integrate the function f(x) = sin(x) over the interval [0, 1], using N = 2,4,8, 16, ..., equally spaced subintervals in [-1,1]. List the observed errors (the difference between the numerical integral and the exact integral) in a Table. How many function evaluations are needed for the error to be less than 10-7 ? Derive the local Three-point Gauss Quadrature Formula for integrating a function f(x) over the reference interval [-1, 1]. (This formula uses the roots of the orthogonal polynomial 3(x).) Use the corresponding composite formula to integrate the function f(x) = sin(x) over the interval [0, 1], using N = 2,4,8, 16, ..., equally spaced subintervals in [-1,1]. List the observed errors (the difference between the numerical integral and the exact integral) in a Table. How many function evaluations are needed for the error to be less than 10-7 ?

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To derive the local Threepoint Gauss Quadrature Formula for integrating a function fx over the reference interval 11 we start by considering the three ... View the full answer