A possible way to integrate dx^2?

  • Thread starter depther
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While reading a proof for an integral equation I came across this formula:
http://imgur.com/K8RQlOc

It was claimed that it can be proven..
 

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  • #2
andrewkirk
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If my calculations are correct, it's either meaningless or false.
It's meaningless if ##dx^n## means ##(dx)^n##
It's false if ##dx^n## means ##d(x^n)##. Counterexample is ##n=2,\ f(x)\equiv 1##. This gives LHS=##t^2-a^2## and RHS=##\frac{1}{2}(t-a)^2##
 
  • #3
HallsofIvy
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I wonder what "x" is supposed to represent. On the left x appears to be an n dimensional vector but on the right it is a number.
 
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