Integral symbol

The integral sign is long from the letter s ("s" ), originated as an abbreviation for the word sum, latin summary. This symbolic notation of integrals goes back to Gottfried Wilhelm Leibniz. For the integral sign there are a number of variations, including for multiple integrals, line integrals, surface integral and volume integral.

History

Leibniz mentioned in a later manuscript to published Analysis tetragonistica from October 29, 1675 for the first time the integral sign. :

" Utile erit scripsisse ∫ per omnia "

" It will be useful to write ∫ instead of omnia "

Omnia stands for omnia l and is used in the geometrically oriented surface calculation method of Bonaventura Cavalieri. The corresponding print publication Leibniz 's De geometria recondita of 1686th At that time he called the integral calculus nor calculus summatorius, so the long S. Even Johann Bernoulli engaged in at the time with the subject, and since Leibniz strove single scientific character, they discussed about. So there was the sign of Leibniz and the name integralis calculus, integral calculus, Bernoulli.

Use

The integral of a real function in the variables over the interval is

Noted. The multiplicative -to-read notation indicates in how the integral operation adds up from strips of height and infinitesimal width to the area under the function.

Traditions of the formula set

In the various traditions of the formula set slightly different forms of the integral sign have naturalized. Thus, in the picture German form of the integral character depicted form is used, while for example in the Russian space itself is a form variant has established that reproduces the graphics Russian variant form of the integral character in the German Formula sentence.

Russian variant form of the integral sign

In addition to write, for example, in the U.S. set in text formulas the upper and lower limits placed on the right of the symbol, to reduce disturbing line spacing,

While in German tradition

Would be usual. Also integrals in text formulas always smaller than in remote formulas.

Coding

The integral sign and its variations are encoded in computer systems follows.