where would trap rule best be applied

where would trap rule be best applied?
Is these right? are there other ones?


1. when integration of a linear equation if diffuclt or cant be done using other technquies

2. when you have sizable quantity of data

If Intervals (ordinates) are small accuracy of result will not be high and trap rule would not be best employeed to determine the result. If you have high quantity of intervals (ordinates), accuracy of the result would be high and the trap rule be best employed.

3. when only set data is avabile and no function is given, it allows for area to still be determined.

The question was

Evaluate the use of various numerical estimation techniques. Indicate where you think
that each technique may be best applied, commenting upon the accuracy of each
technique.


I did accuracy, just on the applied bit

Don't understand what this means. When can't you integrate a linear equation?
Why would this make a difference? You say:

But I'm not clear why this is a specific issue to the trapezium rule.

So does, for example, Simpson's rule.

To be fair, I don't know what the expected answer is. Other things being equal, you'd generally prefer to use Simpson's rule, so personally I'd be looking at the circumstances in which you can use the Trapezium Rule but not Simpson's Rule.

Well, all I've done is comment on what you wrote previously. I don't find your answers convincing, but at the same time, I don't know your syllabus, or the context of the question, etc.
If the only technique you know for approximating an integral is the trapezium rule, it makes it a lot easier to justify using it. But if you know Simpson's rule, it is generally going to be superior, so justifying using the trapezium rule becomes a lot harder.

would a reason for trap rule be
simpsons rule requires even ordinates to be used where as trap can have both

I don't really see the point in such questions...

Nothing like a quick Google for getting information:

See here

Interesting, but at this level I feel the most applicable fact is that Simpson has stricter requirements on the behaviour of the ordinates. (The "smoothness requirement" is something I think could easily be mentioned at A-level, but AFAIK it isn't).

Looking back at the OP's posts on other threads, I get the impression they're at uni. doing engineering; not that there's any clue to that fact in this thread.

"Smoothness" probably isn't too important even then.

An old (2000) engineering book I have mentions ease of programming and computation as one advantage of Trap. over Simpson, but I wouldn't have though that particularly relevant, unless one's working with extremely rapidly changing real time applications, given the processing power available today.

Looking back at the OP's posts on other threads, I get the impression they're at uni. doing engineering; not that there's any clue to that fact in this thread.

"Smoothness" probably isn't too important even then. H

An old (2000) engineering book I have mentions ease of programming and computation as one advantage of Trap. over Simpson, but I wouldn't have though that particularly relevant, unless one's working with extremely rapidly changing real time applications, given the processing power available today.

Hi

Doing it HND online at Unicourse.org
and very little help and the questions paper is written really bad to understand.

Yes. You can also use the trapezoidal rule when your ordinates are uneven (basically do a 2 pt trap calculation on each interval), which you can't do with Simpson.

Would a place you wouldnt use them would be with expontiental functions because they dont naturally follow the curve.