The great secret has already been revealed that this mysterious symbol∫, which is after all only a long S, merely means “the sum of”, or “the sum of all such quantities as”. It therefore resembles that other symbol Σ (the Greek Sigma), which is also a sign of summation. There is this difference, however, in the practice of mathematical men as to the use of these signs, that while Σ is generally used to indicate the sum of a number of finite quantities, the integral sign ∫ is generally used to indicate the summing up of a vast number of small quantities of infinitely minute magnitude, mere elements in fact, that go to make up the total required. Thus ∫dy = y, and ∫dx = x.
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