Consider the following method for approximating f(x) dx. Divide the interval [a,

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Consider the following method for approximating f(x) dx. Divide the interval [a, b] into n equal subintervals. On each subinterval approximate f by a quadratic function that agrees with f at both endpoints and at the midpoint o f the subinterval. Explain why the integral of f on the subinterval [xi, xi+1] is approximately equal to the expression h/3 (f(xi / 2) + 2f (mi) + f(xi + 1) / 2)), where mi, is the midpoint of the subinterval, mi = (xi + xi+1)/2. (See Problem 9.) Show that if we add up these approximations for each subinterval, we get Simpson's rule:

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