Integral Command

Integral[ <Function> ]

Gives the indefinite integral for the given function with respect to the main variable.

Example:

Integral[x^3] yields \frac{x^4}{4}.

Integral[ <Function>, <Variable> ]

Gives the partial integral of the function with respect to the given variable.

Example:

Integral[x^3 + 3 x y, x] yields \frac{x^4 + 6 x^2 y}{4}.

Integral[ <Function>, <Number a>, <Number b> ]

Gives 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> ]

Gives the definite integral of the function, with respect to the main variable, in the interval [a , b] and shadows the related area Evaluate = true. In case Evaluate = false the related area is shaded but the integral value is not calculated.

CAS Syntax

Integral[ <Function f> ]

Gives the indefinite integral for the given function with respect to the main variable.

Example:

Integral[cos(x)] yields sin(x) + c_1.

Integral[ <Function f>, <Variable t> ]

Gives the indefinite integral of the function with respect to the given variable t.

Example:

Integral[cos(a t), t] yields \frac{sin(a t)}{a} + c_1.

Integral[ <Function>, <Number a>, <Number b> ]

Gives the definite integral of the function, with respect to the main variable, in the interval [a , b].

Example:

Integral[cos(x), a, b] yields sin(b) - sin(a).

Integral[ <Function f>, <Variable t>, <Number a>, <Number b> ]

Gives the definite integral in the interval [a , b] with respect to the given variable t.

Example:

Integral[cos(t), t, a, b] yields sin(b) - sin(a).