Ask A Scientist Mathematics Archive

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