Use the error formulas in Theorem 8.6 to find n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using

(a) The Trapezoidal Rule

(b) Simpson’s Rule.

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THEOREM 8.6 Errors in the Trapezoidal Rule and Simpson's Rule If f has a continuous second derivative on [a, b], then the error E in approximating f f(x) dx by the Trapezoidal Rule is |E| ≤ (b − a)³ 12n² |E| ≤ -[max [f"(x)], a ≤x≤ b. Trapezoidal Rule Moreover, if f has a continuous fourth derivative on [a, b], then the error E in approximating fa f(x) dx by Simpson's Rule is (b − a)³ 180n4 -[max f(x)], a ≤ x ≤ b. Simpson's Rule