Use the error formulas in Theorem 8.6 to estimate the errors in approximating the integral, with n = 4, using

(a) The Trapezoidal Rule and 

(b) Simpson’s Rule.

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) 12n |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) 180n4 -[max f(x)], a x b. Simpson's Rule