Relative to the interval [ - 2,2], consider the fixed (open) quadrature points x = -...

 

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Relative to the interval [ - 2,2], consider the fixed (open) quadrature points x = - 2 +kAx, where 4 Ax = 4/5 and k runs from 1 to 4. (a) Write down a linear system of equations defining weights in the quadrature rule Q = 4 E wkf(xx) for approximating k =1 f(x)dx if the rule is to exactly integrate polynomials of highest possible degree (no need to solve the system). (b) If the rule is applied to f(x) =x3 -x +4 then what is the result? Justify your answer. Relative to the interval [ - 2,2], consider the fixed (open) quadrature points x = - 2 +kAx, where 4 Ax = 4/5 and k runs from 1 to 4. (a) Write down a linear system of equations defining weights in the quadrature rule Q = 4 E wkf(xx) for approximating k =1 f(x)dx if the rule is to exactly integrate polynomials of highest possible degree (no need to solve the system). (b) If the rule is applied to f(x) =x3 -x +4 then what is the result? Justify your answer.

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