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

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) [max ["(x)[],_a x b. 12n |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 [(4)(x)]], a x b. Simpson's Rule