MaplePrimes - answers and comments on Question, Problem approximating the arc length of this problem

Problem approximating the arc length of this problem

gkokovidis — Tue, 15 Nov 2011 06:18:25 Z

I am using Maple input in the attached worksheet. I do not see the problem that you are refering to. Every time I run the worksheet, I get the same answer. Notice in the last line, where zero (0) is replaced by zero.zero (0.0). This forces a floating point approximation of the integral, to the default of 10 decimal places.

Download arclengthtrig_eval.mw

Regards,

Georgios Kokovidis

Dräger Medical

erroneous space

acer — Tue, 15 Nov 2011 07:06:18 Z

Your worksheet contains an erroneous space between sin and (5 x) which is causing Maple to think that you have a product of terms sin*(5*x) instead of the desired function application sin(5*x).

Once that erroneous space is removed, then the faulty implicit multiplication instance is removed and your example ought to work as expected.

Please note that, for involved expressions, evalf[5](...) is not a good way to approximate a final result accurate to 5 decimal places. What it does do it make internal numeric computation occur with 5 digits of working precision (possibly with some guard digits for atomic operations). But that is not the same as ensuring 5 places of accuracy for involved, compound expressions. A better approach would be to use evalf at normal working precision, and then only applying evalf[5] to a final floating-point result. This is a common misunderstanding. Your particular example may not be involved enough for this distinction between precision and accuracy to have manifested itself.

acer

Response

JerJohnson123 — Tue, 15 Nov 2011 19:35:58 Z

If thats the case, then how would I find the actual answer? Doing what you suggested in regards to changing sin and (5x) to sin(5 x) gives me this answer when evaluating:

arclengthtrig.mw

disregard my other post

JerJohnson123 — Tue, 15 Nov 2011 19:40:28 Z

Disregard the other post I made. The other user's method seemed to work. Thanks foryour help in the explaination!

Perils of premature reduction of Digits

Doug Meade — Tue, 15 Nov 2011 20:17:41 Z

@JerJohnson123 What acer is saying is that you should have Maple perform the calculations using more digits than you want in your answer. Once the calculations have been done, then you can use evalf[5] to have the answer displayed with 5 significant digits.

To illustrate, consider:

restart;
Digits;
                               10
1 + 1.123456789 - 2.123456;
                                  -7
                           7.89 10  
evalf[5](%);
                                  -7
                           7.89 10  
Digits := 5;
                               5
1 + 1.123456789 - 2.123456;
                               0.

If you have more questions, please ask.

displayprecision

Joe Riel — Wed, 16 Nov 2011 06:25:11 Z

Another possibility is to use the ?interface procedure to set the number of digits that are **displayed**.

interface(displayprecision = 5):

The computation will be carried out using Digits, but ony 5 digits of precision are displayed. That is convenient for typical engineering work.