The Mathematical Symbol "Integral (∫)"

The ∫ Symbol in Mathematics: Integral

The realm of mathematics is teeming with symbols that encapsulate deep and intricate concepts. One of the most recognizable and foundational symbols is the ∫ symbol, denoting the concept of integration. This article will delve into its meaning, core applications, and offer some illustrative examples.

Usage

The ∫ symbol signifies the operation of integration, a foundational concept in calculus. Integration can be viewed as the reverse process of differentiation and is instrumental in finding areas under curves, solving differential equations, and describing accumulated quantities, among other applications.

Examples

  • Example 1: Basic Integration:
    The expression \( ∫ x^2 dx \) represents the integral of \( x^2 \) with respect to \( x \). The result is \( \frac{x^3}{3} + C \), where \( C \) is an arbitrary constant.
  • Example 2: Definite Integral:
    The expression \( ∫_0^1 x^2 dx \) denotes the definite integral of \( x^2 \) from 0 to 1. This computes the area under the curve \( y = x^2 \) between those two bounds, resulting in a value of \( \frac{1}{3} \).

In summary, the ∫ symbol stands as a beacon of calculus, representing the integration operation. Its applications span a wide array of mathematical and real-world problems, making it indispensable in the study and application of mathematics.

Mathematical symbol 'Integral'

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Codes for the ∫ Symbol

The Symbol∫
Alt CodeAlt 8747
HTML Code∫
HTML Entity∫
CSS Code\222B
Hex Code∫
UnicodeU+222B

How To Insert the ∫ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ∫ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8747. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML TextOutput
<b>My symbol: &#8747;</b>My symbol: ∫

(Method 4) Use the HTML Entity Code (for webpages).

HTML TextOutput
<b>My symbol: &int;</b>My symbol: ∫

(Method 5) Use the CSS Code (for webpages).

CSS and HTML TextOutput
<style>
span:after {
content: "\222B";}
</style>
<span>My symbol:</span> 		My symbol: ∫

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x222B;</b>My symbol: ∫
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x222B to place the ∫ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);
Output

∫

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ∫ is U+222B. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
TypeOutput
222B
[Hold down Alt]
[Press x]		∫
(The 222B turns into ∫. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u222B. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u222B"
document.write("My symbol: " + str)		My symbol: ∫