This video shows how to calculate areas bounded by curved lines.
First, I show a simple example of the calculation method.
(F is a variable which contains a data field with values from zero to ten.)
Now I define the variable F. F contains a data field with values from zero to ten.
I insert a chart box, so we can show the results graphically.
In this expression, the goal is to calculate the red area.
We use a similar method as in the integral calculation.
The field is splitted into individual rectangular segments.
The result is the sum of all segments.
Of course we can use a simple method as we have no curved lines.
If we assume that this scale indicates centimeters, we have ten times ten centimeters. So the area is 100 square centimeter. The red area is one hundred divided by two. The result is fifty square centimeters.
But this example is also used to demonstrate the calculation with curved lines.
Here I write down sum of F.
The result is 55. We have a deviation of 5 square centimeters. This is because we calculate the sum of two times one, plus three times one, plus four times one, and so on.
We have calculated a rectangle and the inclined surface is not considered. Thus we have a half square centimeter more in each segment.
To obtain the correct result, we have to compute with mean value. This is 3.5, 4.5, 5.5 and so on.
I define the variable A and use the function average, the short form is a v e r.
Average returns a data field which contains the mean values of the elements from the argument.
Then I change sum F in sum A, RedCrab shows the correct result of fifty.
I change the field F to 360.
Now I define a new variable s. S contains a field whose values are the sine from the elements of F.
I change the chart box reference from f to S.
Now the chart box shows an area with an upper border in form of a sine curve.
I change sum ( a) to sum ( s)
The result of sum is zero, because here we have a value range from 1 to -1. The positive and negative part offset each other.
We have to raise this in the positive range. To do this we write here, plus one.
The result of sum is now 361. We have here again a deviation as we did not use the average.
When I change the argument of sum to ‘a’. And the argument of average to s,
Then we have here the correct result of 360.
Now I change the field limit in F to 150.
The range is positive and I remove plus one from this formula
We have the result of the red area. It is 106.9 square centimeter.