PART A: Write a function in Matlab that computes a numerical integral using the composite Boole's rule with the definition:

function numI = compBoole(f, a, b, N)

where the inputs are:

f: function to be integrated

a, b: left and right interval endpoints (bounds)

N: number of intervals between a and b

numI: the output, or the returned numerical integral

PART B: use this function to compute the integral where

f = e^(-(x^2)/2)

(a, b) = (3,3)

N = 5*(2^k) where k = 1,2,3,4,5

The exact integral is sqrt(2pi)erf(3*sqrt(2)/2) where erf is a matlab built-in function. Print out the number of divided intervals along with the absolute numerical error. Plot the error against the divided interval length (b-a)/N = 6/N using loglog scale. Numerically compute the rate of convergence for this rule. You shall observe the rate is approximately 6.