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Why are the Midpoint, Trapezoidal, and Simpson's Methods necessary? That is, why do we need to be able to numerically approximate integrals?Why not simply integrate

Why are the Midpoint, Trapezoidal, and Simpson's Methods necessary?

That is, why do we need to be able to numerically approximate integrals?Why not simply integrate the expression using the techniques we're learning this week, and evaluate the anti-derivative at the endpoints?

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