Incorrect integral calculation in MuPAD

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Nishant Shankhwar 2015-12-22

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评论： Walter Roberson 2015-12-23

Integration of function x-1 wrt x using command int(x-1,x) in MuPAD gives answer as (x-1)^2/2 instead of x^2/2-x. Can anybody explain why?

Thanks in advance.

Regards Nishant

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Answer 1

Walter Roberson 2015-12-22

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The difference between the two is 1/2 which is a constant and so falls into the usual "plus an arbitrary constant" category. If you diff((x-1)^2/2,x) you get x-1, so you cannot say that the result is incorrect.

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Nishant Shankhwar 2015-12-23

Your argument is correct, but in sympy or maple same integral comes out to be x^2/2-x and diff(x^2/2-x,x) is x-1. Therefore x^2/2-x seems more convincing than (x-1)^2/2.

Walter Roberson 2015-12-23

x^2/2 - x might be more conventional but remember that the indefinite integral is really x^2/2 - x + a constant, so any result of the form x^2/2 - x + a particular constant + an implied constant is mathematically correct

It does look unusual, but the mathematics of it is sound.

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