Consider approximating integrals of the form

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

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

b) To find a fomula which is exact for all polynomials of degrees set up a system of four equations with unknowns w1, w2, x1 and x2.

c) Apply ** and**
to
evaluate

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