Let the function f (x) = x² . 5k (a) Find " f(x)dx by completing the following table using Romberg algorithm. Leave your answer in terms of the unknown variable k. Show all the necessary working...

Extracted text: Let the function f (x) = x² . 5k (a) Find " f(x)dx by completing the following table using Romberg algorithm. Leave your answer in terms of the unknown variable k. Show all the necessary working steps. m=0 m =1 m=2 R(0,0) R(1,0) R(2,0) n=0 R(1,1) R(2,1) n=1 n= 2 R(2,2) (b) Use your answer in (a) to find R(2,2) when k =0.1.