INTEGR returns the integrated value of a function in a two-dimensional space

Syntax

1. INTEGR(Pno%, 2, "ColLab$_1", "ColLab$_2", Mode%=0,1 or 2, X_from, X_to)
2. INTEGR(0, Npoints%, x_1, y_1, x_2, y_2,…, x_n, y_n, , Mode%=0,1 or 2, X_from, X_to)
3. INTEGR(@ObjFn(..), 2, @ObjColPar_1, @ObjColPar_2, Mode%=0,1 or 2, X_from, X_to)
4. INTEGR(Telitab$, 2, "ColLab$_1", "ColLab$_2", Mode%=0,1 or 2, X_from, X_to)

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1. See also Telitab access for a generic description on the use of TeLiTab data
2. Similar to other Data analysis functions, the DISINT is a convenient way to evaluate data. Please also look at these functions for syntax examples
3. INTEGR computes the integral from x=x_from to x=x_to using either:

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1. x_from and x_to should be within the limits of the Telitab data provided
2. 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.
3. Please realise the dataset provided to INTEGR should be a function. Every x-value should have one y-value.

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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.

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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

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