(12 points) Approximate the definite integral below for a - 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.You may find these formulas useful! n(n + 1) k = 2 K= 1 k2 = n(n + 1) (2n + 1) 6 K=1 k 3 = 1 m(n+1)12 2 The Trapezoidal Rule: [f ( ajax = = [ ( x o ) + 2/ ( x1 ) + 2f (x2) + ..+ 2/ (xn-1) +/(xx] where Ax _ 5-Q and x = a + iAx , for Osisn. Error bound for Trapezoidal Rule: | E, | M(b -a) 3 12n2 where M, a positive number, is maximum of the second derivative of / in [a,b]. Simpson's Rule: [ f ( x)dx = = [ (xo ) + 4f ( x ) + 2/ ( x2) + 4f ( x3) + ... + 2f (xx-2) + 4f(x-1 ) + f (x] where Ax = - b-a - and , is even. 72. Error bound for Simpson's Rule: |En| M(b-a)5 180n4 where M, a positive number, is maximum of the fourth derivative of f in [a,b]