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    Gaussian Quadrature



    1. Consider approximating integrals of the form

    I ( f ) = &#8747; &#8730;x f(x)dx

    in which f(x) has several continuous derivatives on [0, 1]
    a. Find a formula

    &#8747; &#8730;x f(x)dx &#8776; w1 f(x1) &#8801; I1( f )

    which is exact if f(x) is any linear polynomial.

    b. To find a formula

    &#8747; &#8730;x f(x)dx &#8776; w1 f(x1) + w2 f(x2) &#8801; I2( f )

    which is exact for all polynomial of degree &#8804; 3, set up a system of four equations with unknown w1, w2, x1, x2 and find the values

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    We need to find two unknowns, the weight and the node ...

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    This solution is comprised of a detailed explanation to answer Gaussian Quadrature problems.