Tool to calculate the integral of a function. The computation of a definite integral over an interval consists in measuring the area under the curve of the function to integrate.

Definite Integral - dCode

Tag(s) : Functions, Symbolic Computation

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

⮞ Go to: Primitives Functions

The integral is the operator of the integration calculation in mathematics.

Integration is generally presented as a method of calculating the *area under the curve* of a function, but it can also be applied to the calculation of surfaces and volumes of solids.

Integral calculus is usually set to an interval and uses function primitives.

Some people talk about *indefinite integrals* to describe *primitive* functions (antiderivative). Definite integrals are integrals over an interval.

To perform an integral calculation (integration), first, calculate the corresponding primitive function.

For a function $ f(x) $ to be integrated over $ [a;b] $ and $ F(x) $ the primitive of $ f(x) $. Then $$ \int^b_a f(x) \mathrm{ dx} = F(b)-F(a) $$

__Example:__ Integrate $ f(x) = x $ over the interval $ [0;1] $. Calculate its primitive $ F(x) = \frac{1}{2} x^2 $ and so integral $$ \int^1_0 f(x) \mathrm{ dx} = F(1)-F(0) = \frac{1}{2} $$

Enter the function, its lower and upper bounds and the variable to integrate, dCode will make the computation automatically.

The complete list of common primitives is available on the function primitives page.

The integration involves the primitives of functions to perform the calculation. Primitives are a tool for calculating integrals.

The integral is the operator of the integration calculation, the derivative is the result of the differential calculation. Integral calculus and differential calculus are the 2 fields of infinitesimal calculus.

Calculation of some forms of integrals involve special functions such as $ E $ and $ F $ which are elliptic integrals or $ I_0, I_n, J_0, J_n, K_0, K_n $ which are Bessel functions.

dCode retains ownership of the "Definite Integral" source code. Except explicit open source licence (indicated Creative Commons / free), the "Definite Integral" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Definite Integral" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Definite Integral" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!

Reminder : dCode is free to use.

The copy-paste of the page "Definite Integral" or any of its results, is allowed (even for commercial purposes) as long as you cite dCode!

Exporting results as a .csv or .txt file is free by clicking on the *export* icon

Cite as source (bibliography):

*Definite Integral* on dCode.fr [online website], retrieved on 2023-09-21,

- Primitive Calculator
- Definite Integral Calculator
- Multiple Integral Calculator
- What is an interval? (Definition)
- How to calculate a definite integral over an interval?
- What is the list of common primitives?
- What is the difference between an integral and a primitive?
- What is the difference between an integral and a derivative?
- What are the functions E, F, I0, K0?

integral,function,integration,integrate,calculus,derivative,antiderivative,primitive

https://www.dcode.fr/definite-integral

© 2023 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback