INTEGR returns the integrated value of a function in a two-dimensional space
Syntax
- INTEGR(Pno%, 2, "ColLab$_1", "ColLab$_2", Mode%=0,1 or 2, X_from, X_to)
- INTEGR(0, Npoints%, x_1, y_1, x_2, y_2,…, x_n, y_n, , Mode%=0,1 or 2, X_from, X_to)
- INTEGR(@ObjFn(..), 2, @ObjColPar_1, @ObjColPar_2, Mode%=0,1 or 2, X_from, X_to)
- INTEGR(Telitab$, 2, "ColLab$_1", "ColLab$_2", Mode%=0,1 or 2, X_from, X_to)
Arguments
- Pno% is the number that refers to the TeLiTab sets in the Data slot. Pno% should be an integer value or a parameter which is assigned an integer value and is the number of the TeLiTab set in the expressions' data slot.
- Npoints% is the number of points (x,y) that are given in direct definition.
- @ObjFn() refers to the Object from which data will be used.
- TeLiTab$ refers to the string parameter that contains the TeLiTab.
- "ColLab$_1" and @ObjColPar_1 refer to the column that will be used as the parameter X in the integration.
- "ColLab$_2" and @ObjColPar_2 refer to the column that will be used as the parameter Y in the integration.
- Mode% is the mode of integration:
- Mode% =0 Riemann
- Mode% = 1 Trapezium
- Mode% =2 Simpson.
- X_from and X_to are the parameters between wich will be integrated.
Remarks
- See also Telitab access for a generic description on the use of TeLiTab data
- Similar to other Data analysis functions, the DISINT is a convenient way to evaluate data. Please also look at these functions for syntax examples
- INTEGR computes the integral from x=x_from to x=x_to using either:
- Mode%=0 -> Riemann (bar-wise) integration
- Mode%=1 -> Trapezium rule
- Mode%=2 -> Simpson rule
- x_from and x_to should be within the limits of the Telitab data provided
- Integration can only be performed in 2D space. Multi-dimensional integration is not (yet) implemented (Ndim% = 2). Multi-dimensional integration can be performed by nested INGER() functions.
- Please realise the dataset provided to INTEGR should be a function. Every x-value should have one y-value.
Examples
Example 1: Telitab in dataslot
In this example, syntax 1 is used.
Let y be defined by
y= INTEGR(1, 2, "XC", "YC", 0, x_1, x_2)
This is the command for a Riemann integral between x_1 and x_2, using the points of the curve in the Dataslot.
The following Telitab set is placed in the Data slot:
|INTEGR1| 0 2 "XC" "YC" "1" 1 1 "2" 2 4 "3" 3 9 "4" 4 16 "5" 5 25 "6" 6 36 "7" 7 49 "8" 8 64 "9" 9 81 "10" 10 100| |
For x_1 = 2.5 and x_2=5, this relation returns
y=28.25.
Remark
In case you apply the symbolic addressing of the columns for the description of the point on the curve or surface to compute the differential for, e.g. "Par_x" and "Par_y", please make sure that your Telitab set contains these names. If not, an error message is generated and the calculation is stopped.
Example 2: Direct Definition
This example will illustrate syntax 2.
In direct definition, the points of the curve are stated in the Relation itself:
INTEGR( Pno%, Npoints%, x_1, y_1, x_2, y_2,…, x_n, y_n, Mode%=0,1 or 2, X_from, X_to)
If Pno%=0 then all x_i and y_i values should be numeric expressions. The minimum number of x,y data points Npoints% in the list is 2 in which case the interpolation (and differentiation) is performed linear.
Let y be defined by
y = INTEGR(0, 4, 1, 1, 2, 4, 3, 9, 4, 16, 1, x_1, x_2)
For x_1=2.5 and x_2=5, this relation returns
y=28.25
Example 3: TeLiTab in object or string
Syntax 3 and 4 are similar to syntax 1, but now existing telitabs are used instead of the dataslot.
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