QUADGK
Updated: 31 March 2014
Use the scalar function QUADGK to evaluate a finite integral. QUADGK uses 21-point Gauss-Kronrod quadrature.
Syntax
SELECT [wctMath].[wct].[QUADGK](
<@Func, nvarchar(max),>
,<@VarName, nvarchar(4000),>
,<@A, float,>
,<@B, float,>)
Arguments
@Func
the function to be integrated. @Func is a string containing any valid TSQL statement which includes a single variable that is the object of the integration. The variable name is defined in @VarName. @Func is of a type nvarchar or of any type which implicitly converts to nvarchar.
@VarName
the TSQL variable name. The variable name must start with '@'. @VarName must be of a type nvarchar or of a type which implicitly converts to nvarchar.
@A
The lower limit of integration. @A must be of a type float or of a type that implicitly converts to float.
@B
The upper limit of integration. @B must be of a type float or of a type that implicitly converts to float.
Return Types
float
Remarks
· If @A not less than @B and error will be returned.
· If @Func contains an undeclared SQL variable and it is not defined in @VarName a NULL will be returned.
Example
In this example we want to evaluate the integral:
SELECT
wct.QUADGK(
'SELECT 1/SQRT(@x)', --@Func
'@x', --@VarName
0, --@A
1 --@B
) as Integral
This produces the following result.
Integral
----------------------
2
In this example we want to evaluate the integral:
SELECT
wct.QUADGK(
'SELECT SQRT(4-POWER(@x,2))', --@Func
'@x', --@VarName
0, --@A
2 --@B
) as Integral
This produces the following result.
Integral
----------------------
3.14159265358979
In this example we want to evaluate the integral:
Note that COSH, the hyperbolic cosine function, and SINH, the hyperbolic sine function, are not a built-in SQL Server functions but are part of the XLeratorDB library.
SELECT
wct.QUADGK(
'SELECT PI()/2e+00*wct.COSH(@x)*SIN(EXP(PI()/2e+00*wct.SINH(@x)))', --@Func
'@x', --@VarName
-2, --@A
2 --@B
) as Integral
This produces the following result.
Integral
----------------------
1.57044006384932
See Also