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