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