NOTE: This is for a math based computer science course

Consider the function f(t) = {sint/t, t notequalto 0, 1, t = 0. Note that f is a continuous function for all t. Let I(x) = integral^x_0 f(t) dt, and J = I(1). (a). Compute approximations to J by trapezoid rule with 1, 3 and 9 equal intervals. Try to use fewest possible time of computing f(t). Show which formula you use. (b). Derive a Richardson extrapolation algorithm which uses trapezoid approximations from a), to obtain better approximations to J. Show which formula you use. Generate the corresponding Romberg triangle