| HTML | Meaning | |
|---|---|---|
| ∫ |
∫∫U+222B |
Integral Symbol The Integral Symbol, denoted as ∫, represents the mathematical operation of integration, which finds the area under a curve. |
| ∬ |
∬U+222C |
Double Integral Symbol Represents the process of integrating a function over two variables, often denoting the volume under a surface in three-dimensional space. |
| ∭ |
∭U+222D |
Triple Integral Symbol Used to integrate a function over three variables, often representing the volume of a solid in three-dimensional space. |
| Δ |
ΔΔU+394 |
Delta Symbol (Change) Represents a change in a quantity. |
| ∂ |
∂∂U+2202 |
Partial Derivative Symbol Represents the partial derivative of a function with respect to one of its variables. |
| ∑ |
∑∑U+2211 |
Summation Symbol Represents the operation of summing a sequence of terms. |
What is the Integral Symbol?
The Integral Symbol, symbolized by ∫, is used in mathematics to denote the operation of integration. Integration is the reverse process of differentiation and is used to find the area under a curve or the accumulation of quantities.
Types of Integrals
There are various types of integrals in mathematics:
- Definite Integral: Has upper and lower limits and yields a numerical value representing the area between the function and the x-axis.
- Indefinite Integral: Does not have set limits and yields a family of functions as its result.
- Line Integral: Represents the integration along a curve in a vector field.
- Surface Integral: Represents the integration over a surface in three-dimensional space.
- Double Integral (∬): Denotes the process of integrating a function over two variables. It is often used to find the volume under a surface in three-dimensional space.
- Triple Integral (∭): Used to integrate a function over three variables, which typically represents the volume of a solid in three-dimensional space.
Applications of the Integral Symbol in Various Fields
The Integral Symbol (∫) and its variants (∬ and ∭) have applications in multiple disciplines:
- Mathematics: Used in calculus to determine areas, volumes, and other properties.
- Physics: Used to solve problems related to motion, energy, waves, and more.
- Engineering: Used in various engineering disciplines for design, analysis, and modeling purposes.
How to Type the Integral Symbols Using Keyboard Shortcuts, Alt Codes, and LaTeX
- Windows: Hold down the Alt key and type the appropriate code on the numeric keypad, then release the Alt key. (The specific Alt code may vary based on font and software.)
- Mac: The specific shortcut might vary. Specialized software or settings might be required.
- Linux: Press Ctrl + Shift + u, then type the Unicode hexadecimal and press Enter.
- HTML: Use the named entity appropriate for each integral symbol or its numeric entity.
- LaTeX: For the single integral, use
\int. For the double integral, use\iint. For the triple integral, use\iiint.
Symbols' Images
