2006-07-15 18:53:18 · 6 answers · asked by Kenneth Koh 5 in Science & Mathematics ➔ Mathematics
The Wikipedia link below gives both names (Trapezium Rule = British) and (Trapezoidal Rule = American). I am American, and in obtaining undergraduate and graduate degrees in engineering, I was never exposed to the British name for this technique. It is great to be exposed to other customs and viewpoints on Yahoo. Unfortunately, this has to include what we Americans would call rude behavior. I'm not sure what the rest of the English-speaking countries would call it....probably "Brilliant!".
I believe the question has already been answered by several posters. The link included below from Wikipedia also has the same answer. Functions which are concave up will result in an overestimate and functions which are concave down will result in an underestimate.
Cheers!
2006-07-15 20:02:19 · answer #1 · answered by SkyWayGuy 3 · 0⤊ 0⤋
Trapezium Rule
2016-11-16 08:26:59 · answer #2 · answered by jackett 4 · 0⤊ 0⤋
Its not the "trapezium rule" but the "trapezoid rule" of numerical integration.
If you know the nature of the curve, then you can guess at the nature of your error. If you are integrating a curve that is concave up, then the trapezoid rule will over-estimate. If its concave down then it will under-estimate. If it has some oscillation then at some sections its over-estimating and at others its underestimating.
My personal favorite method is a combined simpsons rule. Its as fast as it gets, can handle arbitrary numbers of points, and is very acurate. It perfectly integrates cubics.
2006-07-15 19:07:10 · answer #3 · answered by Curly 6 · 0⤊ 1⤋
As mentioned, this function overestimates everywhere f'' > 0 and underestimates everywhere f'' < 0. This is in response to curly - "trapezium rule" is the correct name in great britian and most English-speaking countries. Kindly refrain from assuming that everyone lives in America.
2006-07-15 19:14:01 · answer #4 · answered by Pascal 7 · 0⤊ 0⤋
It depends on the concavity(second derivative) of the equation. If it is positive, you will over-estimate. If it is negative, you will under-estimate.
Consider the area under the curve of a parabola. If the coefficient of x^2 is positive, you will under-estimate
If the coefficient is negative, you will over-estimate
2006-07-15 19:06:48 · answer #5 · answered by PC_Load_Letter 4 · 0⤊ 0⤋
Underestimating, definitely. But it still remains too close to call.
2006-07-15 19:02:01 · answer #6 · answered by Anonymous · 0⤊ 0⤋