What is the reason for this error in the answer?

[dkothia]

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.

[LucMeekes]

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

[dkothia]

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

[LucMeekes]

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

[Fred_Kohlhepp]

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

Symbolic evaluation gives you zero:

[dkothia]

Yaa..thank bro..drinks on me

[MJG]

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