What ∫ means
It means add up continuously across a variable. With lower and upper limits it is a definite integral: the total over that interval. Without limits it is an indefinite integral, a family of antiderivatives plus a constant.
Why does the integral look like a stretched S?
It is Leibniz's long S for summa. Gottfried Leibniz, a co-inventor of calculus, wrote it in private notes in 1675, picturing an integral as a sum of countless thin slices. It first appeared in print in 1684 in Acta Eruditorum, a Latin scholarly journal.
What it means when someone sends it to you
3 readings∫ alone before a function
Find an antiderivative, adding a constant.
∫ with lower and upper limits
Total the function across the interval between those limits.
∫ followed by dx
Integrate with respect to x, the changing variable.
Don't confuse it with
1Questions people ask
1Why does my integral symbol look different in another app?
It can. Plain-text ∫ is drawn by the destination font, while equation editors may use a math-font glyph with different height, slant or spacing.
How to type ∫
Windows (Word)
Alt+XType 222B, then Alt+X to get ∫.
Windows
Win+Rrun charmap for the full table, or use the emoji picker's Ω symbols tab (Win + .).
macOS
Control+Command+SpaceOpen the character viewer and search “integral”.
Linux
Ctrl+Shift+UType 222b, then Enter or Space.
HTML
∫CSS
\222BMicrosoft Word
Insert an equation with Alt+=, type \int and press Space.
LaTeX
Type \int; with limits, \int_a^b.
Linux
Press Ctrl+Shift+U, type 222B, then press Enter.
Codes and encoding1 code points
HTML decimal
∫
HTML hex
∫
CSS content
content: "\222B";
Each escape is closed by the next backslash; a trailing space is needed before a literal hex digit.
URL encoded
%E2%88%AB
1
On screen
1
Code points
1
JS .length
3
UTF-8 bytes
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.