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.

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