# Integral Command

From GeoGebra Manual

Revision as of 12:33, 21 October 2011 by Christina.biermair (talk | contribs)

- Integral[Function]
- Yields the indefinite integral for the given function with respect to the main variable.
**Example:**`Integral[x³]`

yields*x⁴ / 4*.

- Integral[ <Function>, <Variable> ]
- Returns the partial integral of the function with respect to the given variable.
**Example:**`Integral[x³+3x y, x]`

yields*(x² (x² + 6y)) / 4*.

- Integral[Function, Number a, Number b]
- Returns the definite integral of the function, with respect to the main variable, in the interval [
*a , b*]. **Note:**This command also shadows the area between the function graph of*f*and the*x*-axis.

- Integral[Function, Number a, Number b, Boolean Evaluate]
- Returns the definite integral of the function, with respect to the main variable, in the interval [
*a , b*] and shadows the related area when*Evaluate = true*. In case*Evaluate = false*the related area is shaded but the integral value is not calculated.

## CAS Syntax

- Integral[ Function f]
- Yields the indefinite integral for the given function with respect to the main variable.
**Example:**`Integral[cos(x)]`

returns sin(x)+c1.

- Integral[Function f, Variable t]
- Returns the indefinite integral of the function with respect to the given variable
*t*. **Example:**`Integral[cos(a t), t]`

returns sin(a t)/a+c2.

- Integral[Function, Number a, Number b]
- Returns the definite integral of the function, with respect to the main variable, in the interval [
*a , b*]. **Example:**`Integral[cos(x), a, b]`

returns sin(b) - sin(a).

- Integral[Function f, Variable t, Number a, Number b]
- Returns the definite integral in the interval [
*a , b*] with respect to the given variable*t*. **Example:**`Integral[cos(t), t, a, b]`

returns sin(b) - sin(a).