Simpson's rule and trapezoidal rule ?'s

[ryingling5711]

when do you use simpson's rule over trapezoidal rule?

why does simpsons rule alternate 4 and 2?

 

[Robert1986]

when do you use simpson's rule over trapezoidal rule?

why does simpsons rule alternate 4 and 2?

I think, though I could be wrong, Simpson's rule is used when the curve you are approximating is smooth and "parabolicish." The trap rule, on the other hand, should be used then your curve is not so smooth or not so "parbolicish". Both have some sort of error estimate, right? I might go for the one with the lowest estimate.

 

[ryingling5711]

I'm not really sure about that because i know you can use both for parabolic curves so but maybe your right that the trap rule is better for estimating integrals on less parabolic curves.

 

[LCKurtz]

I'm not really sure about that because i know you can use both for parabolic curves so but maybe your right that the trap rule is better for estimating integrals on less parabolic curves.

Generally speaking you would expect better approximations for curvy functions with Simpson's rule. One surprising fact about Simpson's rule is that it is exact for cubics even though by design you might expect it would be exact only for second and lower degree polynomials.