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Definite Integral

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.

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Definite Integral -

Tag(s) : Functions, Symbolic Computation

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# Definite Integral

## Definite Integral Calculator

### Upper bound

 Result Format Automatic Selection Exact Value (when possible) Approximate Numerical Value Scientific Notation

## Multiple Integral Calculator

### What is an interval? (Definition)

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.

### How to calculate a definite integral 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.

### What is the list of common primitives?

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

### What is the difference between an integral and a primitive?

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

### What is the difference between an integral and a derivative?

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.

### What are the functions E, F, I0, K0?

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.

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Definite Integral on dCode.fr [online website], retrieved on 2023-09-21, https://www.dcode.fr/definite-integral

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