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The Algebraic Integral Calculator

A Very Unusual Calculation Device

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This website provides a free calculation device, (The Algebraic Integral Calculator) in the online JavaScript and spreadsheet formats for solving integrals similar to the following:

The online version of the Algebraic Integral Calculator is embedded in this webpage, four paragraphs below.  The download links for the spreadsheet versions of the Calculator are just below the online version.  However, you should read the following before you use the Algebraic Integral Calculator, because it is a very unusual device, but it is easy to use.

What Makes The Algebraic Integral Calculator So Unusual

Generally, integrals are solved for the area under the curve, which is represented by M on the Algebraic Integral Calculator.  However, the Algebraic Integral Calculator solves for the value of B, and the user must provide the values for A, n, and M (see the integral above).  This is useful for checking homework, and similar calculations, after you calculated the area under the curve manually.  The Algebraic Integral Calculator checks its own calculations a fraction of a second after it has calculated the value for B, by calculating the area under the curve using B, A, and n.

The Algebraic Integral Calculator is also useful for anyone that is interested in spreadsheets at an advanced level.  (The Calculator was originally created with Microsoft Excel, but it was converted to JavaScript for online functionality.)  A number of specialized spreadsheet formulas had to be created for the Algebraic Integral Calculator.  These formulas are illustrated, on various sections of the Calculator.  You can copy and modify these formulas, and use them for your own needs.

The Algebraic Integral Calculator has a built-in error checking device, and two extremely sensitive devices that provide readouts indicating the level of computer calculation error.  One of these devices indicates percent of error, and the other indicates percent of accuracy.  If there is a significant level of inaccuracy, in a calculation, the error-checking device displays an error message, instead of calculated results.  This happens when numbers are extremely large or extremely small, when the exponent is excessively large, or when there is no calculated results for the numbers that were entered.

If you want a printer friendly version of the Calculator left click on these words.  (If you print the version presented below, Everything on this webpage will be printed.)

 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 XY-Coordinates for the Area Under the Curve The calculations for the XY-coordinates of the area under the curve from point (A, An ) to point (B, Bn ) 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 X-Y-Coordinates when X=A is calculated below Xa = A = Ya = f(A) = An = X-Y-Coordinates when X=B is calculated below Xb = B = Yb = f(B) = Bn = Note, the area under the curve is calculated in the last section Mechanisms for: Rounding down, Error-Checking, 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 error-checking 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 Error-Checking are rounded to decimal places. This is done, to prevent rounding errors, in the error-checking 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 Error-Checking 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 error-checking 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 error-checking 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: =(CalculatedM-M)/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 =

System Requirements for the

Algebraic Integral Calculator,

System Requirements

The spreadsheet versions of the Algebraic Integral Calculator require either Microsoft Excel, or the OpenOffice.org software package.  In addition, Microsoft Windows is required for the spreadsheet versions.

The JavaScript version of the Algebraic Integral Calculator can run on any operating system that has JavaScript support, but I only tested it with Microsoft Windows.  In addition, the JavaScript version requires a browser that supports JavaScript.  Almost all modern operating systems and browsers support JavaScript.

Algebraic Integral Calculator In the

Microsoft Excel, OpenOffice Calc, And Javascript Formats

If you want the Algebraic Integral Calculator in the Microsoft Excel format, left click on these words.

If you want the Algebraic Integral Calculator in the newer 2007 Microsoft Excel format, left click on these words.  Note, this requires Microsoft Excel 2007 or newer additions of Excel.

If you want the spreadsheet version of the Algebraic Integral Calculator that was used to create the JavaScript version left click on these words.  (This is in Microsoft Excel format.)

If you want the Algebraic Integral Calculator in the OpenOffice Calc format, left click on these words.  This requires the free OpenOffice.org software package.

If you want the online Algebraic Integral Calculator in a printer friendly format, left click on these words.

If you want the Algebraic Integral Calculator in all of the above formats, in a zip folder, left click on these words.

Services Offered by the Author

This website was designed to maximize efficiency and ease-of-use (usability, user-friendliness).  The text is presented with relatively large fonts.  The paragraphs are short, and the sentence structure and wording were written to maximize comprehension*.  The website has a very simple layout, on a single page.  This makes it easy to navigate intuitively, by scrolling down or up.  All the links for downloads and other websites are also written with large fonts, and clearly marked as links, such as with the following words: left click on these words.

Note: The ideas on this website and the Algebraic Integral Calculator are technical, and they require knowledge of calculus.  In addition, some familiarity with spreadsheets and computer technology is also needed for maximum comprehension.

Services Offered by the Author David@TechForText.com

I design and build user-friendly software based calculation devices for arithmetic, accounting, currency exchange rates, algebra, trigonometry, correlations, calculus, and databases with built-in calculation devices.  I also create attractive online calculation devices for websites.  I generally make these devices in the Microsoft Excel, OpenOffice.org, and the JavaScript formats, but I can work with other spreadsheet formats besides the above.

I can create web communication forms for your website.  This includes forms with built-in calculation devices.

I write instructions for the devices I build.  I can also write instructions for software and computer devices created by others.  In addition, I can write advertising for your websites, products and services.

For a list of all the services I offer see www.TechForText.com

For a list of all my websites see www.David100.com

My resume is online at: www.David100.com/R

I can provide the services mentioned above on a fee-for-service basis, or possibly based on temporary or permanent employment.  If you are interested in my services, and want additional contact information or more data on the services I offer, you can email me at David@TechForText.com or use a website communication form, by left clicking on these words.

I am located in the USA.  If you are a great distance from my locality or are in another country, this is not important.  I can provide these services worldwide, because the software and websites I make can be delivered through the Internet to any locality, providing there are no governmental restrictions.

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