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dkothia1-Visitor
1-Visitor
March 30, 2016
Question

What is the reason for this error in the answer?

  • March 30, 2016
  • 6 replies
  • 3758 views

Basically the answer should be a perfect zero (according to theory and also verified through hand calculation), so why this software is giving such high error.

Please tell me if I am doing something wrong as soon as possible.

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6 replies

L
LucMeekes23-Emerald IV
23-Emerald IV
March 30, 2016

Because you are numerically evaluating the integral

The precision with which Mathcad calculates numerical evaluation is in the order of 10^-17.

You're doing nothing wrong. You could set the 'zero tolerance' of numerical calculation to a higher value (e.g. 10^-10) this would show all numbers x with |x|<10^-10 as 0. But it would obscure results that are actually meant to be e.g. 10^-12.

Success!

Luc

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dkothia1-VisitorAuthor
1-Visitor
March 30, 2016

Then what is the solution to this problem, is there any other software with high tolerance value?

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LucMeekes23-Emerald IV
23-Emerald IV
March 30, 2016

This is not a 'problem'. Just be aware that all calculations go with a certain uncertainty/accuracy.

Simply calculate 1/2-1/3-1/6 and see what comes out.Mathcad will tell you:

MsExcell will tell you 0, until you multiply the result with 10^18, then it spits out 27.76

If you want exact answers, use a symbolic engine (Mathcad, Maple, Mathematica, Maxima).

Success!
Luc

P.S. If you want to know why the 'error' is in the order of 10^-17, have a look at:

Numerical Precision in MathCAD

    F
    Fred_Kohlhepp23-Emerald I
    23-Emerald I
    March 30, 2016

    It's numerical evaluation precision error.  (10^-17 is a large error?)

    Symbolic evaluation gives you zero:

    D
    dkothia1-VisitorAuthor
    1-Visitor
    March 30, 2016

    Yaa..thank bro..drinks on me

    M
    MJG1-Visitor
    1-Visitor
    March 30, 2016

    Just change the result formatting from "General" to "Decimal":

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