FunctionMath.Integrate Method

Definition

Namespace: Numerics.NET
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 10.0.0

Overload List

Integrate(Func<Double, Double>, Interval<Double>) Numerically integrates a function of one variable.
Integrate(Func<Double, Double>, Double, Double) Numerically integrates a function of one variable.
Integrate(Func<Double, Double, Double>, Interval<Double>, Interval<Double>) Numerically integrates a function of two variables over a rectangular region.
Integrate(Func<Double, Double>, Double, Double, Boolean) Numerically integrates a function of one variable.
Integrate(Func<Double, Double, Double>, Double, Double, Double, Double) Numerically integrates a function of two variables over a rectangular region.

Integrate(Func<Double, Double>, Interval<Double>)

Numerically integrates a function of one variable.
C# 
public static double Integrate(
	this Func<double, double> integrand,
	Interval<double> interval
)

Parameters

integrand  Func<Double, Double>
A function of one variable that specifies the function to integrate.
interval  Interval<Double>
The integration interval.

Return Value

Double
An approximation of the definite integral of integrand over interval.

Usage Note

In Visual Basic and C#, you can call this method as an instance method on any object of type Func<Double, Double>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).

Integrate(Func<Double, Double>, Double, Double)

Numerically integrates a function of one variable.
C# 
public static double Integrate(
	this Func<double, double> integrand,
	double lowerBound,
	double upperBound
)

Parameters

integrand  Func<Double, Double>
A function of one variable that specifies the function to integrate.
lowerBound  Double
The lower limit of the integration interval.
upperBound  Double
The upper limit of the integration interval.

Return Value

Double
An approximation of the definite integral of integrand from lowerBound to upperBound.

Usage Note

In Visual Basic and C#, you can call this method as an instance method on any object of type Func<Double, Double>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).

Integrate(Func<Double, Double, Double>, Interval<Double>, Interval<Double>)

Numerically integrates a function of two variables over a rectangular region.
C# 
public static double Integrate(
	this Func<double, double, double> integrand,
	Interval<double> xInterval,
	Interval<double> yInterval
)

Parameters

integrand  Func<Double, Double, Double>
A function of two variables that specifies the function to integrate.
xInterval  Interval<Double>
The limits of the integration region in the X direction.
yInterval  Interval<Double>
The limits of the integration region in the Y direction.

Return Value

Double
An approximation of the definite integral of integrand over a rectangle spanned by xInterval in the X direction, and yInterval in the Y direction.

Usage Note

In Visual Basic and C#, you can call this method as an instance method on any object of type Func<Double, Double, Double>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).

Integrate(Func<Double, Double>, Double, Double, Boolean)

Numerically integrates a function of one variable.
C# 
public static double Integrate(
	this Func<double, double> integrand,
	double lowerBound,
	double upperBound,
	bool extrapolate = false
)

Parameters

integrand  Func<Double, Double>
A function of one variable that specifies the function to integrate.
lowerBound  Double
The lower limit of the integration interval.
upperBound  Double
The upper limit of the integration interval.
extrapolate  Boolean  (Optional)
If true, Romberg extrapolation is used to improve the accuracy of the result.

Return Value

Double
An approximation of the definite integral of integrand from lowerBound to upperBound.

Usage Note

In Visual Basic and C#, you can call this method as an instance method on any object of type Func<Double, Double>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).

Integrate(Func<Double, Double, Double>, Double, Double, Double, Double)

Numerically integrates a function of two variables over a rectangular region.
C# 
public static double Integrate(
	this Func<double, double, double> integrand,
	double xLowerBound,
	double xUpperBound,
	double yLowerBound,
	double yUpperBound
)

Parameters

integrand  Func<Double, Double, Double>
A function of two variables that specifies the function to integrate.
xLowerBound  Double
The lower limit of the integration region in the X direction.
xUpperBound  Double
The upper limit of the integration region in the X direction.
yLowerBound  Double
The lower limit of the integration region in the Y direction.
yUpperBound  Double
The upper limit of the integration region in the Y direction.

Return Value

Double
An approximation of the definite integral of integrand over a rectangle from xLowerBound to xUpperBound in the X direction, and from yLowerBound to yUpperBound in the Y direction.

Usage Note

In Visual Basic and C#, you can call this method as an instance method on any object of type Func<Double, Double, Double>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).

See Also