You may find these formulas useful! n(n + 1) K = 2 * = 1 k2 n(n + 1) (2n + 1) 6 k3 = m(n + 1)] 2 The Trapezoidal Rule: [f ( ajdx = = [ ( x o ) + 2f ( x1 ) + 2f (x2 ) + .. + 2/(*n-1) + / (xx] where Ax _ b-a and x1 = a + iAx , for Osisn. Error bound for Trapezoidal Rule: | En | M(b-a) 3 12n2 where M, a positive number, is maximum of the second derivative of / in [a,b]. Simpson's Rule: [ f ( )dx = = [f ( x ) + 4f ( x , ) + 2/ ( x2 ) + 4f ( xg) + ".. + 2f (in-2) + 4f (xm-1 ) + f (x ] where Ax = - b-a 72 and a is even. Error bound for Simpson's Rule: |En| M(b-a)5 18074 where M, a positive number, is maximum of the fourth derivative of f in [a,b].\f(12 points) Approximate the definite integral below for n = 4 by using a) Trapezoidal rule b) Simpson's rule " Give a bound on the error of estimates for both methods in parts a and b. 5 h 1=4. O