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Card 11 / 11:
Simpson’s rule
a rule that approximates ∫ a b f ( x ) d x using the integrals of a piecewise quadratic function. The approximation S n to ∫ a b f ( x ) d x is given by S n = Δ x 3 ( f ( x 0 ) + 4 f ( x 1 ) + 2 f ( x 2 ) + 4 f ( x 3 ) + 2 f ( x 4 ) + 4 f ( x 5 ) + ⋯ + 2 f ( x n − 2 ) + 4 f ( x n − 1 ) + f ( x n ) ) trapezoidal rule a rule that approximates ∫ a b f ( x ) d x using trapezoids
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