Integral – Meaning, Copy & Paste, LaTeX, Unicode
Complete mathematical reference, typing shortcuts, character entities, and usage guide for the Integral (∫).
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What Does the ∫ Symbol Mean?
The integral symbol (∫) represents the continuous accumulation of quantities, such as calculating the area under a curve, volume, displacement, or total accumulation. It is the fundamental operator of integral calculus, invented by Gottfried Wilhelm Leibniz as an elongated 'S' for summa.
Real Numeric Examples
∫ 2x dx 2 · (x² / 2) + C = x² + C The indefinite integral of 2x with respect to x. Using the power rule of integration, the antiderivative is x² plus an arbitrary constant of integration C.
∫_{0}^{3} 3x² dx [x³]_{0}^{3} = 3³ - 0³ = 27 - 0 A definite integral evaluated from 0 to 3. The antiderivative of 3x² is x³, so evaluating between bounds yields 27.
LaTeX, Unicode, HTML & Keyboard Codes for ∫
Copy individual technical codes and character entities with one click:
\int U+222B ∫ ∫ Alt+8747 Option + B How to Type ∫ on Every Device and Application
Step-by-step instructions for Windows, Mac, Word, Google Docs, Excel, HTML, LaTeX, and mobile devices:
Windows
Hold down Alt and type 8747 on the numeric keypad, or type 222B in Word and press Alt + X. You can also press Win + . to pick it from the Symbols tab.
Alt+8747 Mac (macOS)
Press Option + B on standard US/UK Mac keyboards to instantly insert ∫, or open Character Viewer with Cmd + Ctrl + Space.
Option + B Microsoft Word
Press Alt + = to enter Equation Mode, type \int, and press Space. Or type 222b followed by Alt + X.
\int Google Docs
Go to Insert > Equation, type \int, and press Space. You can also go to Insert > Special characters and search 'integral'.
\int Excel / Spreadsheets
Insert into any cell using the formula =UNICHAR(8747), or copy and paste ∫ directly.
=UNICHAR(8747) HTML & Web
Use the HTML named entity ∫ or the numeric entity ∫.
∫ LaTeX (Math Mode)
Write \int in math mode. For definite integrals with bounds, write \int_{a}^{b} f(x)\,dx.
\int Android & iPhone (iOS)
Copy ∫ from this page and paste it into mobile notes, messaging, or math apps.
∫ Commonly Confused With
Distinguish ∫ from visually similar mathematical glyphs and characters:
Double Integral
vs ∫The single integral (∫) calculates area under 1D functions, while the double integral (∬) integrates over a 2D surface area.
Explore in calculus symbolsContour Integral
vs ∫The contour integral (∮) denotes line integration along a closed loop or path, indicated by the circle across the integral sign.
Explore in calculus symbolsEsh (IPA)
vs ∫The phonetic letter Esh (ʃ, U+0283) represents the 'sh' sound in the International Phonetic Alphabet, whereas ∫ (U+222B) is the mathematical calculus operator.
Explore in calculus symbolsFrequently Asked Questions About ∫
Answers to common questions about typing, meaning, and syntax for ∫:
What is the historical origin of the integral symbol ∫?
The symbol was introduced in 1675 by Gottfried Wilhelm Leibniz. It is an elongated Latin letter 's', standing for 'summa' (Latin for sum), reflecting Leibniz's view of integration as an infinite sum of infinitesimal rectangles.
How do you type ∫ in Word?
In Microsoft Word, hit Alt + = to open the Equation Editor, type \int, and press Space. Or type the hex code 222B and immediately hit Alt + X.
How do you write a definite integral in LaTeX?
In LaTeX, use \int with subscript for the lower limit and superscript for the upper limit: \int_{0}^{\pi} \sin(x)\,dx.
What is the Excel formula to display the integral symbol?
In Excel or Google Sheets, enter =UNICHAR(8747) to dynamically output the ∫ character into a spreadsheet cell.