Gauss QuadratureChapter 22.4Newton-Cotes the integralwas determined by calculating the area under the curveconnecting points a and b (where we evaluate the function at the end points)..

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Gauss Quadrature

Consider 2 points along a straight line in between a and b where positive and negative errors balance to reduce total error and give a an improved estimate of the integral.

Uses unequal non-uniform spacing best for functions not tabular data.

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*Gauss Quadrature - Method of undetermined Coefficients

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*Two Point Gauss Legendre FormulaExtend the method of undetermined coefficients:

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*We now have 4 unknowns , need 4 equations!Two Point Gauss Legendre Formula

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*Example 1 Evaluate the integral ofUsing Gauss Legendre

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*Exercise 1 Evaluate the integral ofUsing Gauss Legendre

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