Integral Command

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).