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Date: Around 1993


Question:
Does the integral of x^2(dx)^.5 have any meaning? If it does, how does one go about integrating the expression?



Replies:
I am not familiar with any meaning for this, but if we change it slightly to x^2*d(x^.5), then substitution methods do apply, etc. In the usual sense of the definition of differentials, (dx)^.5 will never appear, so something other than Riemannian Integration would have to be defined to give this a foundation.

Tom Elsner


There is something called "fractional integration," which I remember hearing about many years ago. You could try and find a book on this. It is based on a relation between multiple integration of one-dimensional functions and the B-function (sorry, I forgot the proper name). Anyway, I do not recall that fractional integrals were actually very useful.

Arthur Smith



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