The following results were obtained in a certain experiment. x 0 1.50 3 4.5 67.5 9 10.5 12 f(x) 230 345 456 537 520 763 863 965 1070 a) Use order of h6 Romberg's algorithm (level 3) to find an approximate value of the area bounded by the unknown function represented by the table and the lines x = 0, x = 12. 12 (i.e. estimate f(x) dx) b) Use the above table to determine df(x) dx at x = 0 of accuracy of O(h²), with h = 1.5.