definite and indefinite integration
int(expression, [x, y, ...], options)
int(expression, [x = a..b, y = c..d, ...], options)
algebraic expression; integrand
names; variables of integration
a, b, c, d
endpoints of interval on which integral is taken
(optional) various options to control the type of integration performed. For example, numeric=true will perform numeric instead of symbolic integration. See int/details for more options.
The int(expression, x) calling sequence computes an indefinite integral of the expression with respect to the variable x. Note: No constant of integration appears in the result.
The int(expression, x = a..b) calling sequence computes the definite integral of the expression with respect to the variable x on the interval from a to b.
The int(expression, [ranges or variables]) calling sequence computes the iterated definite integral of the expression with respect to the variables or ranges in the list in the order they appear in the list. Note: The notation int(expression, [x = a..b, y = c..d]) is equivalent to int(int(expression, x = a..b), y = c..d) except that the single call to int accounts for the range of the outer variables (via assumptions) when computing the integration with respect to the inner variables.
You can enter the command int using either the 1-D or 2-D calling sequence. For example, int(f,x) is equivalent to ∫fⅆx.
If any of the integration limits of a definite integral are floating-point numbers (e.g. 0.0, 1e5 or an expression that evaluates to a float, such as exp(-0.1)), then int computes the integral using numerical methods if possible (see evalf/int). Symbolic integration will be used if the limits are not floating-point numbers unless the numeric=true option is given.
If Maple cannot find a closed form expression for the integral (or the floating-point value for definite integrals with float limits), the function call is returned.
Note: For information on the inert function, Int, see int/details.
No constant of integration appears in the result for indefinite integrals.
f ≔ 7⁢x3+3⁢x2+5⁢x:
If Maple cannot find a closed form expression for the integral, the function call is returned.
Compute definite integrals.
An Elliptic integral
A double integral
If either of the integration limits are floating-point numbers, then int computes the integral using numerical methods.
An integral with decimal limits using numerical methods:
To apply symbolic integration methods instead, use numeric=false:
The option numeric=true or simply numeric may also be used to compute a numerical integral even with exact limits:
For detailed information including:
Integration involving Units
Integration over a complex interval
Inert form of the int command, Int
see the int/details help page.
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