Numerical Approximation of the Definite Integral

[Guest]

Numerical Approximation of the Definite Integral:

In regards to the Trapezoidal Rule, Simpson's Rule or Riemann's Sum, which method is the most accurate?

thank you in advance

 

[stapel]

I would think that this would depend upon the function being integrated, the interval over which it was being integrated, the number of sub-intervals, and the particular sub-interval endpoints being chosen.

Eliz.

 

[pka]

Almost any current calculus text will discuss the relative merits of each method.
If you have access to the calculus text by James Stewart, he does a good job of comparing the errors in each method.

 

[Guest]

thank you both

I would tend to agree more with Stapel though.

 

[stapel]

Re: thank you both

I would tend to agree more with Stapel though.

I said "it depends", and pka said "and Stewart does a nice job of explaining how and why". Where is the difference in what we said?

Eliz.