
The Algebraic Integral Calculator:
Simple Three Step Instructions 


1) To enter or delete
numbers, left click with the mouse on the relevant white input
box. 


2) Delete the numbers in the following three
white input boxes, and enter your own numbers. 


3) For results, left click with the mouse on
the calculation button, or yellow background. 


The exponent: n = 



Area under the curve: M = 



A = 



The Algebraic Integral Calculator was created
in Microsoft Excel, and it was converted to JavaScript. The
formulas used to create this software are shown in the Excel format for
illustration purposes. 

In the white input boxes, n, M,
and A, were defined with the name mechanism in Microsoft Excel.
As a result, the letters are recognized by the computer, in terms
of the numbers entered in the input boxes. 

This provides the functionality needed for
creating spreadsheet formulas using letters and/or words. 

B is the Calculated Result 
An integral is usually solved for the area under
a curve, but that is NOT what we are doing here. We are
calculating the value of B 



B = 



The Numbers in red type, are
calculated results, or numbers transmitted from one cell to
another by this software. 


A fraction of a second after calculating the
value for B, this software calculates the area under the curve, (from B to
A) to check the calculated results. 



M = 




This software compares the calculated area, and
the area entered by the user, to determine the accuracy of
calculations. 




A = 









The spreadsheet formulas from above are
presented below, (with their error messages). 

For B
=IF((ABS(C50)>L45),"NO CALCULATED RESULT FOR THE NUMBERS YOU
ENTERED",ROUND(B, M42)) 
0 
The above displays the value of B, but B is
calculated elsewhere, with this formula: =(M*(n+1)+A^(n+1))^(1/(n+1))


For A =IF((ABS(C51)>L46), "NO CALCULATED RESULT",
ROUND(A, M42)) 

For M =IF( (ABS(C51)>L46), "NO CALCULATED RESULT",
ROUND(M, M42)) 

Calculations for the
XYCoordinates for the Area Under the Curve 




The calculations for the XYcoordinates of the
area under the curve from 



point (A, A^{n
}) to point (B, B^{n }) are carried out by the
software, with the 



numbers that were entered by the user, which
are listed below: 


Number entered by user A = 




This is a calculated result
B = 



Number entered by user n = 




















The curve is produced by this equation:
Y 
= X 




XYCoordinates when X=A is calculated
below 



X_{a} = A 
= 




Y_{a} = f(A) = A^{n} 
= 



XYCoordinates when X=B is calculated below




X_{b} = B 
= 




Y_{b} = f(B) = B^{n} 
= 



Note, the area under the curve is
calculated in the last section 


Mechanisms for: Rounding down, ErrorChecking,
Measuring Error and Accuracy 


All of the numbers ABOVE are automatically
rounded to 

decimal places. 


You can increase or decrease the number of
decimal places, by deleting the 


blue number, above, and entering the number of
decimal places you prefer 

When numbers have 

decimal places, or less, they are
not rounded. 

Note, the errorchecking device, presented
below, has its own rounding mechanism. 

In general, computer calculations are usually
accurate to at least 10 or 15 decimal places. However, with
certain number combinations, or when many digits are 


involved, there may be a lower level of
accuracy. The Algebraic Integral Calculator has a user
controllable mechanism, below, to prevent the display of calculation



results that deviate from accuracy by a
specific percentage. 


Calculated result with an error greater than 

will NOT be displayed. 

If you want a greater or lesser level of
acceptable error, delete the blue number, 


above, and enter the number you prefer.
The smaller the number, the greater the 


accuracy. The number you enter can be a
decimal, such as 0.001 % or it can 


even be zero. 


All of the numbers for the ErrorChecking are
rounded to 

decimal places. 


This is done, to prevent rounding errors, in
the errorchecking mechanism. 


You can increase or decrease the number of
decimal places, by deleting the 


blue number, above, and entering the number of
decimal places you prefer. 


If you enter a number that is too
large, you will see rounding errors. 


Note, this rounding mechanism does not affect
the number of zeros displayed. 

The ErrorChecking and Measuring Mechanism of
the Algebraic Integral Calculator 




This device calculates the error in percent,
which is presented below in red type. 





Spreadsheet formula (Percentage Format) for
above is: =ROUND( (CalculatedM M)/M, M55 ) 




The above errorchecking and measuring
mechanism functions by comparing the value the user entered for the area
under the curve, and the calculated value for the area 


under the curve. In the formulas,
M is the value the user entered for the area, and the calculated value for
the area is represented by CalculatedM. This can be seen
above 


in the spreadsheet formula, and in
the conventional formulas presented below. 


Keep in mind that the values the
user entered were used to calculate B. Then the calculated area was
obtained using the values for B, A, and n. 



















The above formula, and errorchecking device
measures the degree of error. Low numbers, or zero means
little or no error. 






The following device and related formula are
similar to the above, except it calculates the degree of
accuracy, instead of the degree of error. The device and the
formula, 


calculate accuracy by dividing the
calculated area, (CalculatedM) by the area the user entered (M).
This ratio is multiplied by100% This can be seen in
the following formula. 


















With the above formula, and the device
presented below, the higher the number, the greater the accuracy.
A perfectly accurate calculation is 100% accurate. 





This device calculates the percent of accuracy






Spreadsheet formula (in Percentage
Format) for above is: =(CalculatedMM)/M 























The Area Under the Curve is 


In this section, the calculated results, and
numbers obtained from other sections of the calculator are NOT rounded down to a predetermined
number of decimal places. 

This is because the numbers are used for
additional calculations, on several sections of the Calculator.







The spreadsheet formula for the following
is =(M*(n+1)+A^(n+1))^(1/(n+1)) 



The value of B was defined below, with the
Microsoft Excel name mechanism 



B= 






Below, is the calculated value of
the area under the curve, based on the calculated value for B.
This is the calculated value of M, and it is 



defined as: CalculatedM with the Excel name
mechanism. 


















The spreadsheet formula for the
above is: =(( B^(n+1)  A^(n+1) )/(n+1)) 





This formula calculates the area under the
curve. 




A = 





















