If f has a continuous second derivative on [a, b], then the error E in approximating is |E| ≤ (b-a)³ 12n² Moreover, if f has a continuous fourth derivative on [a, b], then the error E in approximating |E| ≤ -[max [f"(x)], a≤ x ≤ b. (b - a) 5 180n4 1 1 + x [max [f(4)(x)], a ≤x≤ b. dx ["F(x) (a) Trapezoidal Rule n = f(x) dx by the Trapezoidal Rule is Use these to find the minimum integer n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using the Trapezoidal Rule and Simpson's Rule. 4 (b) Simpson's Rule n = [ F(x) f(x) dx by Simpson's Rule

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