You can calculate numerical integrals, derivatives (dy/dx) and x-axis intercepts with any X-Y style chart. In
addition, you can find intersection points of dual function plots.

Use the Calc button, below the chart, to select from available options.
Integral Calculations
You can calculate the integral, with respect to x, for a given range of an X-Y plot. Select the applicable
integral option using the Calc button. You will be prompted for the x value range over which the
calculation is to be performed.
The integral represents the area between the curve and the x-axis over the specified range, and the result
will be displayed to an estimated number of digits of accuracy. The accuracy will be determined by the number of
plotted data points, and where there are few data points and potential accuracy is low, an error range will also
be shown with the result, for example: "2.3 +/-0.1".
In making this calculation, it is assumed that function plots show smoothly varying trends, whereas this
assumption is optional for X-Y data plots (see below).
Derivative Calculations
You can calculate the gradient of an X-Y plot at a given value of x. Select the applicable derivative option
using the Calc button. You will be prompted for the x value at which the gradient dy/dx is to be
found.
The result will be displayed to an estimated number of digits of accuracy.
In making this calculation, it is assumed that function plots show smoothly varying trends, whereas this
assumption is optional for X-Y data plots (see below).
Plot dy/dx Tracing
The gradient at the plot tracer position is also shown in the trace box beneath the chart. You will see this
update as you move the mouse over a plot. This is calculated to the precision allowed by the size of the chart
window, and should be treated as an approximate value only. You can use the Calc button to find more
accurate results.
Finding Intersection Points
You can find x-axis intercepts for any plot, and points of intersection where two function plots are
displayed on the same chart. If there is more than one intersection between the plots, you will be prompted for
which point to find. In this case, input "1" for the first point, or "2" for the second etc.
The result will be displayed to an estimated number of digits of accuracy. The accuracy will be determined by
the number of plotted data points, and where there are few data points and potential accuracy is low, an
indication will be shown to signify the approximate nature of the result.
Notes. Intersection points are determined using a numerical method which cannot usually find
intersection points where the area of intersection is zero. Also note that in making the calculation, it is
assumed that function plots show smoothly varying trends, whereas this assumption is optional for X-Y data plots
(see below).
Accuracy and the Smooth Data Assumption
When performing calculations with X-Y list data, it will be assumed by default that the data describes a
smoothly varying trend. You can, however, turn on or off this setting from the Calc button. This setting
will affect the results and accuracy of integral and derivative calculations.
Consider the chart below, which shows an X-Y data plot of only a few points.

Here we can see that the area beneath the trapezium is calculated to be 2.3. However, we may have initially
expected the result to be precisely 2.0, i.e. the area of the trapezium (1 + 3) × 1/2 = 2.0.
In effect, what has been calculated is an estimate for the area of a curve passing through the points,
rather than a trapezium. The error value "+/-0.1" shown is an indication that there are insufficient points to
fix the curve accurately.
If you are displaying X-Y list data, you can turn off this assumption setting from the Calc button in
the lower part of the Chart Window (uncheck "Assume Smooth Data"). Re-calculating the above result in this case,
will yield a value of 2.0, rather than 2.3.
Calculations using the Function Graph always assume that the underlying
trend is smooth.
See also: Graphing a Function, and Graphing Examples.
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