__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 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

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

__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 need additional information on __downloading,__
left click on the Google search link, below:

Google Search:[How to download files from the Internet]

__Download Links, for the Microsoft Excel____ Format__

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

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

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

__Download Links,
for the ____OpenOffice Calc Format__

* *

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

__Download Links,
for the JavaScript____ ____Version__

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

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

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

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

__Download Link, for
All of the above, in One Zipped Folder__

__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 Generator__. ** Under
each
integral** you will see the following words, with the spreadsheet
formula:

* *

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

__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__

__Design Concept to
Maximize User‑Friendliness: For the Website and For
The Basic Integral Calculus Generator____.__

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**

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

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

**Simple Four Step Instructions
for
the Basic Integral Calculus Generator**

**Downloads and Related Information
for
the Basic Integral Calculus Generator**

**Download Links,
for
the Microsoft Excel**** Format**

**Download Links,
for
the ****OpenOffice Calc Format**

**Download Links,
for
the JavaScript**** Version**

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

**Creating
the Basic Integral Calculus Generator**

**The
Excel
Version Was Created First**

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

**Creating Graphics
for
the Basic Integral Calculus Generator with MathType**

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

**The Design Concepts,
and
Services Offered by the Author**

**Services
Offered
by the Author David Alderoty**

** **