# Integral Command

From GeoGebra Manual

- Integral( <Function> )
- Gives the indefinite integral with respect to the main variable.
**Example:**`Integral(x^3)`

yields x^4 \cdot 0.25.

- Integral( <Function>, <Variable> )
- Gives the partial integral with respect to the given variable.
**Example:**`Integral(x³+3x y, x)`

gives*\frac{1}{4}x^4 + \frac{3}{2} x² y*.

- Integral( <Function>, <Start x-Value>, <End x-Value> )
- Gives the definite integral over the interval
*[Start x-Value , End x-Value]*with respect to the main variable. **Note:**This command also shades the area between the function graph of*f*and the*x*-axis.- Integral( <Function>, <Start x-Value>, <End x-Value>, <Boolean Evaluate> )
- Gives the definite integral of the function over the interval
*[Start x-Value , End x-Value]*with respect to the main variable and shades the related area if*Evaluate*is*true*. In case*Evaluate*is*false*the related area is shaded but the integral value is not calculated.

## CAS Syntax

In the CAS View undefined variables are allowed as input as well.

**Example:**`Integral(cos(a t), t)`

yields \frac{sin(a t)}{a} + c_1.

Furthermore, the following command is only available in the *CAS View*:

- Integral( <Function>, <Variable>, <Start x-Value>, <End x-Value> )
- Gives the definite integral over the interval
*[Start x-Value , End x-Value]*with respect to the given variable. **Example:**`Integral(cos(t), t, a, b)`

yields - sin(a) + sin(b).

**Note:**

- The answer isn't guaranteed to be continuous, eg
`Integral(floor(x))`

, that is the integral of the function ⌊x⌋ - in that case you can define your own function to use eg`F(x)=(floor(x)² - floor(x))/2 + x floor(x) - floor(x)²`

, i.e. the function \frac{⌊x⌋² - ⌊x⌋}{2} + x \cdot⌊x⌋ - ⌊x⌋² - in some versions of GeoGebra, a numerical algorithm is used so integrating up to an asypmtote or similar eg
`Integral(ln(x), 0, 1)`

won't work. In this case try`Integral(ln(x), 0, 1, false)`