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Wiris Integrations
Analysis
Reading time: 2minThese commands allow you to analyse the behaviour of functions using tools from calculus. They support symbolic and numerical operations such as derivatives, integrals, and limits, as well as operations that approximate values or define regions between curves. These tools are useful for building exercises involving rates of change, accumulated quantities, and graphical interpretations of functions.
Tip: For practical examples showing how these commands are used in exercises, see the Examples section.
Function Reference
differentiate
Description
Computes the derivative of a function. It can be used to compute higher-order derivatives and to specify the variable with respect to which the differentiation is performed.
Syntax
differentiate(Function)
differentiate(Function, Identifier)
differentiate(Function, Identifier, Integer)
differentiate(Function, Integer)Returns
The symbolic derivative of the function. If an integer n is provided, the result is the n-th derivative.
Notes
- If the variable is omitted, the system assumes the default variable of the function.
- Higher-order derivatives are specified using the integer parameter.
integrate
Description
Computes the integral of a function. The command supports both indefinite integrals (primitives) and definite integrals between two bounds.
Syntax
integrate(Function)
integrate(Function, Identifier)
integrate(Function, Identifier, Integer | Expression, Integer | Expression)
integrate(Function, Integer | Expression, Integer | Expression)Returns
The primitive function for indefinite integration, or the numerical or symbolic value of the definite integral between the specified bounds.
Notes
- Definite integrals require lower and upper limits.
- Bounds may be integers or expressions.
limit
Description
Computes the limit of a function or expression as the variable approaches a specified value.
Syntax
limit(Function, Identifier, Real | Infinity)
limit(Function, Real | Infinity)Returns
The limit of the function as the variable approaches the specified value.
Notes
- The limit point may be a real value or infinity.
- If the variable is omitted, the system assumes the default variable.
numerical_differentiation
Description
Computes the derivative of a function numerically at a specific point.
Syntax
numerical_differentiation(Function, Real)Returns
A numerical approximation of the derivative of the function at the specified value.
Notes
- This method is useful when the derivative cannot be computed symbolically.
- The result is an approximation based on numerical evaluation.
numerical_integration
Description
Computes the value of a definite integral numerically between two points.
Syntax
numerical_integration(Function, Real, Real)Returns
A numerical approximation of the integral of the function between the given bounds.
Notes
- This command is useful when an analytical integral is difficult or impossible to compute.
- The result represents an approximation of the accumulated value between the two bounds.
region
Description
Defines the region between one or two curves. This command can be used to specify areas in the coordinate plane, optionally restricted to a specific range.
Syntax
region(Curve)
region(Curve, Range)
region(Curve, Curve)
region(Curve, Curve, Range)Returns
A region representing the area enclosed by the specified curve or curves, optionally restricted to the provided range.
Notes
- If two curves are provided, the region represents the area between them.
- The optional range
x0..xfrestricts the region to a specific interval.