In Exercises use the error formulas in Theorem 4.20 to estimate the errors in approximating the integral, with n = 4, using 

(a) The Trapezoidal Rule

(b) Simpson's Rule.

Data from in Theorem 4.20

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THEOREM 4.20 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 sa f(x) dx by the Trapezoidal Rule is |E| ≤ - (b − a)³ [max [ƒ"(x)[],_a ≤x≤ b. 12n² |E| ≤ Moreover, if f has a continuous fourth derivative on [a, b], then the error E in approximating f f(x) dx by Simpson's Rule is (b − a)5 180n4 Trapezoidal Rule -[max [ƒ(4)(x)]], a ≤ x ≤ b. Simpson's Rule