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∫
The sign of the integral ( ∫ ) is used to denote the integral in mathematics . It was first used by a German mathematician and one of the founders of differential and integral calculus by Leibniz at the end of the 17th century .
The symbol "∫" was formed from the letter ſ ( "long s" ; from the Latin. Summa ( summa ) - sum) [1] .
Content
Unicode
| Sign | Unicode | Title | HTML view | LaTeX | |||
|---|---|---|---|---|---|---|---|
| Position | Title | Hexadecimal | Decimal | Mnemonics | |||
| ∫ | U + 222B | integral | Integral | & # x222b; | & # 8747; | & int; | \ int |
| ∬ | U + 222C | double integral | Double integral | & # x222c; | & # 8748; | \ iint | |
| ∭ | U + 222D | triple integral | Triple integral | & # x222d; | & # 8749; | \ iiint | |
| ∮ | U + 222E | contour integral | Contour integral | & # x222e; | & # 8750; | \ oint | |
| ∯ | U + 222F | surface integral | Surface integral | & # x222f; | & # 8751; | \ oiint (esint package required) | |
| ∰ | U + 2230 | volume integral | Volume Integral | & # x2230; | & # 8752; | \ oiiint (esint package required) | |
| ∱ | U + 2231 | clockwise integral | Right Bypass Integral | & # x2231; | & # 8753; | ||
| ∲ | U + 2232 | clockwise contour integral | Right-side loop integral | & # x2232; | & # 8754; | \ ointclockwise (esint package required) | |
| ∳ | U + 2233 | anticlockwise contour integral | Left loop contour integral | & # x2233; | & # 8755; | \ ointctrclockwise (esint package required) | |
| ⨋ | U + 2A0B | summation with integral | & # x2a0b; | & # 10763; | |||
| ⨌ | U + 2A0C | quadruple integral operator | Fourfold integral | & # x2a0c; | & #; | ||
| ⨍ | U + 2A0D | finite part integral | & # x2a0d; | & # 10764; | |||
| ⨎ | U + 2A0E | integral with double stroke | & # x2a0e; | & # 10765; | |||
| ⨏ | U + 2A0F | integral average with slash | & # x2a0f; | & # 10766; | |||
| ⨐ | U + 2A10 | circulation function | & # x2a10; | & # 10767; | |||
| ⨑ | U + 2A11 | anticlockwise integration | Left Bypass Integral | & # x2a11; | & # 10768; | ||
| ⨒ | U + 2A12 | line integration with rectangular path around pole | & # x2a12; | & # 10769; | |||
| ⨓ | U + 2A13 | line integration with semicircular path around pole | & # x2a13; | & # 10770; | |||
| ⨔ | U + 2A14 | line integration not including the pole | & # x2a14; | & # 10771; | |||
| ⨕ | U + 2A15 | integral around a point operator | & # x2a15; | & # 10772; | |||
| ⨖ | U + 2A16 | quaternion integral operator | & # x2a16; | & # 10773; | |||
| ⨗ | U + 2A17 | integral with leftwards arrow with hook | & # x2a17; | & # 10774; | |||
| ⨘ | U + 2A18 | integral with times sign | & # x2a18; | & # 10775; | |||
| ⨙ | U + 2A19 | integral with intersection | & # x2a19; | & # 10776; | |||
| ⨚ | U + 2A1A | integral with union | & # x2a1a; | & # 10777; | |||
| ⨛ | U + 2A1B | integral with overbar | & # x2a1b; | & # 10778; | |||
| ⨜ | U + 2A1C | integral with underbar | & # x2a1c; | & # 10779; | |||
Drawing Traditions
The Russian-language tradition of marking the integral sign differs from that adopted in some Western countries.
In the English-language tradition implemented in the LaTeX system, the symbol is substantially inclined to the right.
The German form of the integral is vertical.
In Russian-language literature, the symbol looks like this.
Notes
- ↑ Florian Cajori. A history of mathematical notations. - Courier Dover Publications, 1993 .-- P. 203. - 818 p. - (Dover books on mathematics). - ISBN 9780486677668 .
See also
- The history of mathematical notation
Literature
- Aleksandrova N.V. History of mathematical terms, concepts, notation: Dictionary-reference. - St. Petersburg: LCI, 2007 .-- 248 p.