5.The following results were obtained in a certain experiment. x f(x) 0 5 1 6 2 8 3 15 4 25 5 6 7 8 36 49 65 83 Use Romberg's algorithm to find an approximate value of the area bounded by the unknown function represented by the table and the lines x=0, x-8 and the x-axis. Hint: The Romberg algorithm produces a triangular array of numbers, all of which are numerical estimates of the definite integral (f(x)dx. The array is denoted by the following notation: R(1,1) R(2,1) R(2,2) R(3,1) R(3,2) R(3,3) R(4,1) R(4,2) R(4,3) R(4,4) R(1,1) = [f(a)+ f(b)] | n=24-2 where R(k,,1) = 2 a+(2n-1)Hk) 2n-DH.)]; R(k-11)+HΣf(a+(2n− R(k, j) = R(k, j-1)+- n=1 - R(k,j-1) R(k-1, j-1) 4--1 b-a Hk 24-1