Mathematics-Monster.com
(#mm)

menu

Integral

The Mathematical Symbol "Integral (∫)"

homesitemapsymbolsintegral

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'

Are You Good at Mathematical Symbols?

Do you know, or can you guess, the technical symbols? Well, let's see!
gold cup
Gold

gold cup
Silver

gold cup
Bronze

0
  • This test has questions.
  • A correct answer is worth 5 points.
  • You can get up to 5 bonus points for a speedy answer.
  • Some questions demand more than one answer. You must get every part right.
  • Beware! Wrong answers score 0 points.
  • 🏆 If you beat one of the top 3 scores, you will be invited to apply for the Hall of Fame.
Scoring System

Guru (+)
Hero (+)
Captain (+)
Sergeant (+)
Recruit (+)

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: ∫

You might also like...

Help Us Improve Mathematics Monster

  • Do you disagree with something on this page?
  • Did you spot a typo?
Please tell us using this form.

Find Us Quicker!

  • When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add #mm to your search term.

Share This Page

share icon

If you like Mathematics Monster (or this page in particular), please link to it or share it with others.

If you do, please tell us. It helps us a lot!

Create a QR Code

create QR code

Use our handy widget to create a QR code for this page...or any page.

next up:

Infinity (∞)

More about Mathematical Symbols

Mathematics is a universal language that is used to describe and understand the intricacies of the universe. At the heart of this language are symbols, concise representations that convey specific meanings and ideas.

Just as letters come together to form words in spoken languages, mathematical symbols combine to form expressions and equations, encapsulating intricate ideas in a compact form. The history of these symbols is as varied as their meanings; some have been in use for centuries while others have been introduced more recently to describe new discoveries and concepts. Whether you are a student, educator, researcher, or simply curious, this list of mathematical symbols will serve as a guide, shedding light on their meanings, origins, and applications.

From the simple plus and minus signs to the more esoteric and complex, each symbol has its unique story and significance.

More Symbols

Full List of Mathematical Symbols