# Integral Command

##### Command Categories (All commands)

Integral( <Function> )
Gives the indefinite integral with respect to the main variable.
Example: Integral(x^3) yields \mathrm{\mathsf{ 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 \mathrm{\mathsf{ \frac{1}{4}x^4 }} + \mathrm{\mathsf{ \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 \mathrm{\mathsf{ \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 \mathrm{\mathsf{ - 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 \mathrm{\mathsf{ \frac{⌊x⌋² - ⌊x⌋}{2} + x \cdot⌊x⌋ - ⌊x⌋² }}
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