# Integral Command

##### Command Categories (All commands)

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).
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