A software based calculation device to help students Practice Solving Basic Integrals

Created by David Alderoty © 2011, e-mail David@TechForText.com

To contact the author use the above email address, or

left click on these words for a website communication form.

This website provides, free of charge, the Basic Integral Calculus Generator, which is a software based calculation device, designed to help students practice solving basic integrals.  The Basic Integral Calculus Generator, is available for download in JavaScript, Microsoft Excel, and OpenOffice Calc.  In addition, there is an online version of the Basic Integral Calculus Generator, embedded in this webpage, below the instructions.  (The Excel and OpenOffice Calc versions require Microsoft Windows, but the JavaScript and online version should work with any modern operating system, such as Macintosh and Linux, but it was only tested with Windows.)

If you want to download the Basic Integral Calculus Generator, or want additional information, scroll all the way down, beneath the online version.  Alternatively, you can go to the hyperlinked table of contents of this website, by left clicking on these words.

Primary Purpose, and Instructions for the Basic Integral Calculus Generator

The Basic Integral Calculus Generator is designed for students that know the basic method of solving a simple integral, but need practice to avoid errors, and to increases speed and efficiency with these calculations.  The Basic Integral Calculus Generator is not designed to teach calculus, or to explain related mathematical principles.  If you need this type of instruction, you should do a Google search for videos for basic Calculus.

Simple Four Step Instructions for the Basic Integral Calculus Generator

The Basic Integral Calculus Generator is very easy to use, as explained in the following four steps.

Step one) The user enters two numbers in two white input boxes, located on the upper portion of the Basic Integral Calculus Generator.  The user can choose any numbers he or she prefers.  The numbers can be randomly chosen, and they can even contain decimals.

Note-One) The software generates twelve practice exercises with the numbers entered by the user.  If these numbers are more than two or three digits, the arithmetic might be quite difficult.  If you want arithmetic that is easy, enter single digit numbers.

However the basic Integral Calculus Generator is designed to handle numbers with many digits.  When numbers are extremely large or small they are displayed in scientific notation, using the letter e.  An example of a large number in this format is 4.4218961132108144e+116, and an example of a very small number displayed in this format is 2.5746740266666662e-130 these numbers were actually calculated by the software.  If they were written out in conventional notation, they would be well OVER 100 digits in length.

Note-Two) The numbers that the user enters are applied to twelve integrals, as values for a and b, such as   The software automatically solves the twelve integrals as soon as the numbers are entered, but the calculated results are initially concealed from the user.

Step two) After entering the numbers in the white input boxes, scroll down and you will see 12 integrals, which progressively increase in difficulty.  The student's job is to solve each integral with pencil and paper.  A calculator can be used for the arithmetic.

Step three) After attempting to solve each integral, the student checks his/her pencil and paper calculations, with the result calculated by the software.  To do this there is a simple mechanism under each integral, consisting of a pink box with the letter N in it.  When the user deletes the N, the software displays the calculated result.

Step four) For each practice session, change the numbers in the white input boxes, if you want a set of twelve integrals that have calculated results that are different than the integrals in your previous practice session.  Keep in mind that multiple practice sessions are usually required to master a mathematical technique.

 The Basic Integral Calculus Generator A software-based calculation device to help students Practice Solving Basic Integrals Created by David Alderoty © 2011, e-mail David@TechForText.com To use this software follow the four steps listed below Step 1) In the two white boxes below, enter any two numbers you prefer. With these numbers, the software will generate twelve math problems involving the integral. If you want to keep the arithmetic simple, enter single-digit numbers. Step 2) Scroll down and solve each integral with pencil and paper. You can use a calculator for the arithmetic. Step 3) After attempting to solve each integral, check your calculations with the software. To do this there is a pink box under each integral with the letter N in it. Left click on the box, and delete the N, and the software will display the calculated result for the integral. Step 4) To master a mathematical technique, it is usually necessary to carry out several practice sessions. With this software, you can change the numbers in the white input boxes, for each practice session, so that the integrals will have different calculated results for each session. Below there are two white input boxes. Before you enter or delete numbers in a box left click on it, and then immediately type or delete the number. a = b = Problem 1 a = b = To see calculated result for the above delete the The spreadsheet formula for this calculation is =a-b Problem 2 a = b = To see calculated result for the above delete the The spreadsheet formula for this calculation is =((a^2)-(b^2))/2 Problem 3 a = b = To see calculated result for the above delete the The spreadsheet formula for this calculation is =((a^3)-(b^3))/3 Problem 4 a = b = To see calculated result for the above delete the The spreadsheet formula for this calculation is =((a^4)-(b^4))/4 Problem 5 a = b = To see calculated result for the above delete the The spreadsheet formula for this calculation is =((a^5)-(b^5))/5 Problem 6 a = b = To see calculated result for the above delete the The spreadsheet formula for this calculation is =((a^6)-(b^6))/6 Problem 7 a = b = To see calculated result for the above delete the The spreadsheet formula for this calculation is =((2*a+a^2)-(2*b+b^2))/2 Problem 8 a = b = To see calculated result for the above delete the The spreadsheet formula for this calculation is =((3*a+a^3)-(3*b+b^3))/3 Problem 9 a = b = To see calculated result for the above delete the The spreadsheet formula for this calculation is =((4*a+a^4)-(4*b+b^4))/4 Problem 10 a = b = To see calculated result for the above delete the Spreadsheet formula for this calculation is ((5*a+a^5)-(5*b+b^5))/5 Problem 11 a = b = To see calculated result for the above delete the Spreadsheet formula for this calculation is ((6*a+a^6)-(6*b+b^6))/6 Problem 12 a = b = To see calculated result for the above delete the Spreadsheet formula for this calculation is =((7*a+a^7)-(7*b+b^7))/7

Downloads and Related Information for the Basic Integral Calculus Generator

Step 1) Left click with the mouse on a blue download *link, for the Basic Integral Calculus Generator and a dialog box will open, with an option to save the file.

*Note the download links are located in the next subsection.

Step 2) Save the file on the Windows Desktop or in the Documents Folder, or anywhere else on your computer, where you can easily locate the file’s icon.  Keep in mind that after you downloaded the file, you must locate the file's icon on your computer.

Step 3) The file's icon can be moved after downloading to any location on your computer, with the windows cut and paste function.  You should move the icon to a location on your computer where you can easily find it.  For most people, the best place to store these files is in the Documents Folder (also called the My Documents in some versions of Windows).

An alternative to the above three steps, is to download the Basic Integral Calculus Generator in a zipped folder.  To do this left click on a link with the words: zipped folder.  With this method, most browsers display the files icon as soon as the download is completed.  Then you can use the Windows cut and paste function, to place the file anywhere you want on your computer.

If you want the Basic Integral Calculus Generator, in the newer Microsoft Excel format, left click on these words.  This requires Microsoft Excel 2007, 2010 or later versions, and Windows.

If you want the above in a zipped folder, left click on these words.

If you want the Basic Integral Calculus Generator that was used to create the JavaScript version, left click on these words.  This requires Microsoft Excel 2007, 2010 or later versions, and Windows.

If you want the above in a zipped folder left click on these words.

If you do not have Microsoft Excel on your computer, the best alternative is to use OpenOffice Calc, for the Basic Integral Calculus Generator.  To do this, you must first obtain the FREE OpenOffice.org software package, which provides almost the same functionality as Microsoft Excel, Word, PowerPoint and Access.  The OpenOffice.org software package is open-source, and you can download it from the following website: www.OpenOffice.org

If you do not have Microsoft Windows on your computer, you can use the JavaScript version of the Basic Integral Calculus Generator.  The JavaScript version should work with most modern operating systems, but it was only tested with Windows.

The following two JavaScript versions are in the Web Archive, Single file, format, and they were converted to this format with the save function in Internet Explorer.  This file format is different than the conventional HTML, and it has the extension .mht.  The primary advantage of this file format is it combines the graphics and computer code into one file.  With conventional HTML, the graphics can easily get disconnected from the file, if it is not carefully stored in one folder.   Web Archive, Single file is supported by most of the popular browsers, such as Firefox, Chrome, and Opera, but I was unable to open this file format with SeaMonkey, version 2.  It will be easier to download the following two JavaScript files, in a zipped folder, if you are not familiar with the save function in your browser.

If you want to download the Basic Integral Calculus Generator, in the JavaScript format, left click on these words.  When the file opens you must save it with the save function in your browser, as Web Archive, Single file.   These additional steps are unnecessary if you download the file in a zipped folder

If you want the above in a zipped folder, left click on these words.

If you want to download a printer friendly version,( without background colors) of the Basic Integral Calculus Generator, in the JavaScript format, left click on these words.  When the file opens you must save it with the save function in your browser, as Web Archive, Single file.  These additional steps are unnecessary if you download the file in a zipped folder

If you want the above in a zipped folder, left click on these words.

If you want to open an online version of the Basic Integral Calculus Generator, in the JavaScript format, left click on these words.  This is in conventional HTML format.

If you want to open a printer friendly, online JavaScript version, of the Basic Integral Calculus Generator, left click on these words.  This is in conventional HTML format, and it does not have background colors.

If you want to download the above in a zipped folder left click on these words.

If you want all of the above in one zipped folder, including Excel, Calc, and JavaScript versions of the Basic Integral Calculus Generator, left click on these words.

Creating the Basic Integral Calculus Generator

The Excel Version Was Created First

The Basic Integral Calculus Generator was initially created in Microsoft Excel.  To do this, spreadsheet formulas had to be created for each of the 12 integrals.  The formulas were created by solving the integrals with symbolic notation, consisting of the letters: a and b.  The values of a and b are defined when the user enters two numbers in the input boxes of the Basic Integral Calculus Generator.  The input boxes, were defined with the Microsoft Excel name function, as a and b.  If this was not done, the formulas I created would not be recognized by Microsoft Excel.

After solving the integrals in terms of a and b, it was necessary to modify the results, in terms of notation, to create spreadsheet formulas.  For example, in the spreadsheet notation for Microsoft Word, and OpenOffice Calc, for multiplication the asterisk (*) is used, and for division the slash (/ ) is used.  For squares, square roots, cube roots, etc. the following format in red type is used:          ,

If you want to see the twelve spreadsheet formulas I created, examined the Basic Integral Calculus GeneratorUnder each integral you will see the following words, with the spreadsheet formula: The spreadsheet formula for this calculation is

The spreadsheet formulas I created might look quite different than the conventional calculations used to solve integrals.  However, once you become familiar with the notation, you will see that the formulas are mathematically identical to the conventional way of solving integrals.

Incidentally, with the technique described above, spreadsheet formulas can be created from most conventional formulas, or from almost any mathematical sequence, that can be expressed in terms of letters.  However, when the spreadsheet formulas are written in terms of letters, the related input cells must be defined in terms of the letters.  For example, a spreadsheet formula for area can be written as =L*W, such that L= length, and W= width.  This formula requires that an input cell is renamed or defined as L, and another input cell is renamed or defined as W.

The Creation of the Switching Mechanism, to Conceal or Display Calculated Results

The mechanism That initially conceals the calculated results, as explained above, consists of a pink box with the letter N.  When the student deletes the N, the calculated results for the integral, is displayed.  I created this mechanism with the IF FUNCTION ( IF(  ) ) available in Microsoft Excel, and other spreadsheet software.  Specifically, I created a conditional statement for each integral, consisting of the following: if there is an N in Cellx, do not display the calculated results, but if this is not the case display the results.  (Cellx is used in this explanation to represent any relevant cell on a spreadsheet.)  The actual statement is not written with conventional English wording.  It is written as follows
=IF(Cellx= “N”,  “ ”,  (a formula for integral) )

Creating Graphics for the Basic Integral Calculus Generator with MathType

The graphics for the Basic Integral Calculus Generator are the twelve integrals.  Creating mathematical notation especially integrals, that will display on a website without imperfections is somewhat of a challenge.  All of the websites I have seen to date display mathematics with less than perfect notation.  Integrals and square roots are often displayed in a text format, using the characters on the keyboard.  I actually use a format that is very similar to this to write spreadsheet formulas, but displaying mathematics in this way, is a less than optimal way of conveying mathematical concepts.

In theory, mathematical symbols, including integrals can be displayed on webpages with computer code, which is the same way that text is usually displayed.  However, Internet browsers, as well as the operating systems used in modern computers, universally have the capability of interpreting computer code for text, but this is not the case with mathematical symbols.  There is of course computer code that can display mathematical symbols, if the user has the appropriate software.

I have MathType version 6.7, and it can generate computer code that will display mathematical symbols, but I did not consider this an option, because the Internet browsers do not universally support this type of code, at this point in time.  This will probably change over the next few years.  My only other option was to use a graphics format, to display mathematical notation.  This essentially involves formats that are similar to, or even identical to, the format used in digital photography.  MathType, and even Microsoft Word, and Excel can be used to produce mathematical symbols in of graphic format.

My initial attempts to use graphics to display mathematical notation was less than perfect.  Specifically, when I converted a Microsoft Excel device to JavaScript, with SpreadsheetConverter, the results were aesthetically unfavorable.  Imperfections were apparent, consisting of fine lines where the graphics were inserted, but this was not seen in the Microsoft Excel device before conversion.  The graphics in the JavaScript devices sometimes displayed other imperfections, such as blurriness.

I carried out a series of trial and error experiments, and I found that the best option is to use MathType, and configure it to produce high quality mathematical notation in the Graphics Interchange Format.  Specifically, I set the controls in MathType to produce the GIF format at 360 dpi.  I inserted the resulting graphics into the Microsoft Excel device, one integral at a time.  I then reduced the size of each integral, and carefully placed it in the proper location on the spreadsheet.

Creating graphics that are larger than necessary, and reducing the size when inserting is consistent with good quality.  Just the opposite is also true, creating graphics that are small, and increasing size when inserting is likely to result in a poor quality image.

I have found for conventional webpages, where there is no conversion process to JavaScript, the best and simplest option is the new equation editor in Microsoft word 2010.  This provides the convenience of writing a document with explanatory text and conventional mathematical notation in a single process.  The resulting Microsoft Word document, with the mathematical notation, can easily be converted to a conventional webpage, by saving it in an HTML format, with the save function in Microsoft Word.  This is the technique I use to create this website.

Creating the OpenOffice Calc and JavaScript Versions of the Basic Integral Calculus Generator

After completing the Basic Integral Calculus Generator in the Microsoft Excel format, I electronically converted it to OpenOffice Calc file format, with the save function in the OpenOffice Calc software.  I created the JavaScript version, with SpreadsheetConverter, which generates JavaScript code from an Excel device.  The JavaScript code was edited slightly, and I copied and pasted it into this webpage, with an HTML editor, to create the online version of the Basic Integral Calculus Generator.

I also created JavaScript versions of the Basic Integral Calculus Generator that are especially suitable for printing, and for downloading.  The version for printing is similar to the JavaScript version embedded in this webpage, except it is provided as a separate webpage, to prevent the printing of unwanted text, from the website.  For downloading, I created two JavaScript versions that are in the Web Archive, Single file format.  This file format incorporates all the computer code, including the JavaScript, and the graphics into a single file.  With conventional HTML, the graphics are retained as separate files.

The Design Concepts, and Services Offered by the Author

I designed the Basic Integral Calculus Generator, and this website, in a way that would maximize efficiency and ease-of-use.  The Basic Integral Calculus Generator has instructions placed next to related input cells, and it is laid out with a simple structure, with large fonts.  The website similarly has large fonts, with a similar structure, and clearly written instructions.  For example, the download links on this website contain precise wording, to prevent confusion, such as: If you want the Basic Integral Calculus Generator in the Excel format, left click on these words.

The website is on one long webpage.  This provides the convenience of scrolling down or up, from one section to another, and it avoids the unnecessary complexity of pull-down menus, and links to go from one page to another.  However, I provided a hyperlink table of contents as an alternative way of navigating the website.

Some of the material on this website is technical.  Thus, for an optimum level of comprehension, the reader IDEALLY should have an advanced background in spreadsheets software, coupled with knowledge of programming concepts and calculus.  However, I structured each sentence with the goal of minimizing confusion, and maximizing comprehension, for users with varying levels of technical knowledge.  In this regard, perfection is never possible, because users come from diverse technical, cultural, and linguistic backgrounds.

I provided many headings and subheadings throughout this text.  This allows the user to easily skip material that they find difficult, or uninteresting.  The headings and subheadings are also displayed in the table of contents.

Services Offered by the Author David Alderoty

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 also create web communication forms in JavaScript for websites.  This includes forms with built-in calculation devices.  For a list of websites with calculation devices that I created, left click on these words, or go to the following website: www.TechForText.com/Math

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.

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.

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

My name is David Alderoty, and I am located in the USA, New York City.  If you are a great distance from my locality or are in another country, this is not important.  I can provide the above services worldwide, because the software and the writing services I offer can be delivered through the Internet to any locality, providing there are no governmental restrictions.

Introduction to The Hyperlink Table of Contents of this Website

This website is more or less laid out like a book, but it is on one long webpage.  You can scroll up or down to go from one topic to another.  However, if you want to examine all the sections and subsections of this website, use the hyperlink table of contents, below this paragraph.  To go to any section or subsection of this website you can left click on the blue words that relate to the material you want to read.  The yellow highlighted words are sections, and the un-highlighted words are subsections.

If you want to go to the top of the website, left click on these words.

Table of Contents of this Website

Contents

The Basic Integral Calculus Generator 1

A software based calculation device to help students Practice Solving Basic Integrals  1

Primary Purpose, and Instructions for the Basic Integral Calculus Generator 3

Simple Four Step Instructions for the Basic Integral Calculus Generator 4

The Online Basic Integral Calculus Generator, Is Presented Below, and it Functions Directly From this Webpage. 8

Downloads and Related Information for the Basic Integral Calculus Generator 12

Download Link, for All of the above, in One Zipped Folder 21

Creating the Basic Integral Calculus Generator 22

The Excel Version Was Created First 22

The Creation of the Switching Mechanism, to Conceal or Display Calculated Results. 25

Creating Graphics for the Basic Integral Calculus Generator with MathType  26

Creating the OpenOffice Calc and JavaScript Versions of the Basic Integral Calculus Generator 32

The Design Concepts, and Services Offered by the Author 34

Design Concept to Maximize User‑Friendliness: For the Website and For The Basic Integral Calculus Generator. 34

Services Offered by the Author David Alderoty  37