Let I = 1/2 -1/2 1-a dr. By using the composite trapezoidal rule T(h) with step length h you get the following results h 2 2 2 T(h) 1.2071 1.2650 1.2802 a) Make a regularity check and then use Romberg's method to improve the approximations in the table. Regularity check: Compare T(2h)-T(4h) with T(h) - T(2h) T(2/4) - T(2/2) T(2/8) T(2/4) b) Based on the Romberg table, how many correct decimals does the approximation in a) have? c) Show that I = 4 2 + through a geometric argument (Tip: I's value corresponds to the area in the figure below).