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“Differentiation is mechanics; integration is art.”

• gxs 8y ago
  This is exactly right. You have to get creative sometimes. I was excited as a kid when I was able to get integral(cos(x^(1/2))) - literally jumping up and down.
• abetusk 8y ago
  "Nature laughs at the difficulties of integration." [1] [1] https://en.wikiquote.org/wiki/Pierre-Simon_Laplace https://en.wikiquote.org/wiki/Pierre-Simon_Laplace
• enriquto 8y ago
  > Differentiation is mechanics; integration is art. This is silly. In symbolic calculus, there are well-known algorithms for computing the primitive of any expression (and to decide whether it exists or not). In numerical calculus, integration is actually much easier than derivation.
• commandlinefan 8y ago
  As I was studying math, I noticed this as a trend: somebody defines addition, and everything works fine until somebody comes along and suggests "inverse addition" which introduces this whole new class of numbers that we call "negative numbers". Somebody else defines multiplication and everything's fine, it can even be worked to account for negative numbers... until somebody suggest inverse multiplication which introduces the complexity of this whole new classification of numbers called rational numbers. Somebody defines square roots and now we have irrational and even _imaginary_ numbers. And, of course, somebody defines differentiation and everything is completely straightforward until somebody else defines inverse differentiation and we have this whole class of, while not numbers, problems that are intractable.
  • rm445 8y ago
    It's a nice thought, but I recall reading elsewhere that integration was developed separately to differentiation (to find areas and volumes) until they were found to be related.