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In my opinion (and I'm just a physicist, not a math major) the use of units should be independent of the functional form or the numerical method of integration. Simply adding identical units in the numerator and denominator of the function to be integrated changes the value of the integral. In the real world, the units should simply cancel each other out.
Not only that, but changing the flavor of the units (i.e changing from, say, length units to mass units) in the numerator and denominator ALSO changes the value. Make the units, say, kilometers, then change them both to kilograms- the integral evaluates differently.
Does MathCad change the integration algorithm based on the type of units used ?? That would be special... Some programmer would have to go to a lot of trouble for that implementation.
Remember - the units are IDENTICAL in the numerator and denominator, resulting in a dimensionless function !
Not only that, but changing the flavor of the units (i.e changing from, say, length units to mass units) in the numerator and denominator ALSO changes the value. Make the units, say, kilometers, then change them both to kilograms- the integral evaluates differently.
Does MathCad change the integration algorithm based on the type of units used ?? That would be special... Some programmer would have to go to a lot of trouble for that implementation.
Remember - the units are IDENTICAL in the numerator and denominator, resulting in a dimensionless function !