f is defned by f(x) =
3e^(cos x). graphs of f and its first four
derivatives on the interval [2; 7] are given. Asume that the graphs
are correct.
Suppose I is the value of integral(f(x) dx) from [2 7]
1)Use the graph of f alone to estimate I
Do I just simply sketch and use trap., or midpoint method or something?
2)Use the information in the graphs to tell how many subdivisions N are needed so that the Trapezoid Rule approximation TN will approximate I with error < 10^-5.
I know that Error (TN) < [K(2)*(b-a)^3]/(12*N^2) where K(2) is a number such that |f"(x)|< K(2) . So, do I find K(2) and solve for N or something?
3) Use the information in the graphs to tell how many subdivisions N are needed so that the Simpson's Rule approximation SN will approximate I with error < 10^-5.
Once again, I know Error(SN) < [K(4)*(b-a)^5]/(180*N^4) but dont know where to go from there.
I'll appreciate any help, thanks