Paul's Online Math Notes
Home
Content
Chapter/Section
Downloads
Misc Links
Site Help
Contact Me
Close the Menu
Cheat Sheets & Tables
Algebra, Trigonometry and Calculus cheat sheets and a variety of tables.
Class Notes
Each class has notes available. Most of the classes have practice problems with solutions available on the practice problems pages. Also most classes have assignment problems for instructors to assign for homework (answers/solutions to the assignment problems are not given or available on the site).
Algebra
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Calculus I
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Calculus II
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Calculus III
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Differential Equations
[
Notes
]
Extras
Here are some extras topics that I have on the site that do not really rise to the level of full class notes.
Algebra/Trig Review
Common Math Errors
Complex Number Primer
How To Study Math
Close the Menu
Current Location : Calculus I (Practice Problems) / Extras / Proof of Various Integral Properties
Calculus I
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Review
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Review : Functions
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Review : Inverse Functions
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Review : Trig Functions
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Review : Solving Trig Equations
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Review : Trig Equations with Calculators, Part I
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Review : Trig Equations with Calculators, Part II
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Review : Exponential Functions
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Review : Logarithm Functions
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Review : Exponential and Logarithm Equations
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Review : Common Graphs
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Limits
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Tangent Lines and Rates of Change
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
The Limit
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
One-Sided Limits
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Limit Properties
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Computing Limits
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Infinite Limits
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Limits At Infinity, Part I
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Limits At Infinity, Part II
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Continuity
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
The Definition of the Limit
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Derivatives
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
The Definition of the Derivative
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Interpretation of the Derivative
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Differentiation Formulas
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Product and Quotient Rule
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Derivatives of Trig Functions
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Derivatives of Exponential and Logarithm Functions
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Derivatives of Inverse Trig Functions
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Derivatives of Hyperbolic Trig Functions
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Chain Rule
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Implicit Differentiation
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Related Rates
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Higher Order Derivatives
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Logarithmic Differentiation
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Applications of Derivatives
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Rates of Change
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Critical Points
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Minimum and Maximum Values
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Finding Absolute Extrema
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
The Shape of a Graph, Part I
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
The Shape of a Graph, Part II
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
The Mean Value Theorem
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Optimization
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
More Optimization Problems
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
L`Hospital`s Rule and Indeterminate Forms
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Linear Approximations
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Differentials
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Newton`s Method
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Business Applications
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Integrals
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Indefinite Integrals
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Computing Indefinite Integrals
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Substitution Rule for Indefinite Integrals
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
More Substitution Rule
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Area Problem
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Definition of the Definite Integral
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Computing Definite Integrals
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Substitution Rule for Definite Integrals
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Applications of Integrals
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Average Function Value
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Area Between Curves
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Volumes of Solids of Revolution / Method of Rings
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Volumes of Solids of Revolution/Method of Cylinder
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
More Volume Problems
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Work
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Extras
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Proof of Various Limit Properties
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Proof of Various Derivative Properties
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Proof of Trig Limits
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Proofs of Derivative Applications Facts
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Proof of Various Integral Properties
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Area and Volume Formulas
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Types of Infinity
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Summation Notation
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Constant of Integration
[
Notes
]
[
Practice Problems
]
[
Assignment Problems
]
Close the Menu
If you know exactly which file you'd like to download or you want a file different from any listed below you can go directly to the
Download Page
to get it.
Calculus I
- Complete book download links
Notes
File Size : 3.96 MB Last Updated : Wednesday August 30, 2017
Practice Problems
File Size : 572 KB Last Updated : Monday December 5, 2016
Practice Problems Solutions
File Size : 4.9 MB Last Updated : Monday January 23, 2017
Assignment Problems
File Size : 888 KB Last Updated : Monday June 6, 2016
Extras
- Complete chapter download links
Notes
File Size : 571 KB Last Updated : Saturday July 22, 2017
Proof of Various Integral Properties
- Complete section download links
Notes
File Size : 145 KB Last Updated : Tuesday April 29, 2008
Close the Menu
Contact Me
- Send me an email!
Request Permission for Using Notes
- If you are an instructor and wish to use some of the material on this site in your classes please fill out this form.
Download Page
- This will take you to a page where you can download a pdf version of the content on the site. Note that if you are on a specific page and want to download the pdf file for that page you can access a download link directly from "Downloads" menu item to the left.
FAQ
- A few frequently asked questions.
Links
- Links to various sites that I've run across over the years.
My Students
- This is for students who are actually taking a class from me at Lamar University.
Privacy Statement
- Privacy statement for the site.
Site Help
- A set of answers to commonly asked questions. Note that these are identical to those in the "Site Help" menu.
Site Map
- A full listing of all the content on the site as well as links to the content.
Terms of Use
- Terms of Use for the site.
Close the Menu
The equations overlap the text! What can I do to fix this?
Show Answer
If the equations are overlapping the text (they are probably all shifted downwards from where they should be) then you are probably using Internet Explorer 10 or Internet Explorer 11. To fix this problem you will need to put your browser in "Compatibly Mode" (see instructions below). Alternatively, you can view the pages in Chrome or Firefox as they should display properly in the latest versions of those browsers without any additional steps on your part.
Put Internet Explorer 10 in Compatibility Mode
Look to the right side of the address bar at the top of the Internet Explorer window. You should see an icon that looks like a piece of paper torn in half. Click on this and you have put the browser in Compatibility View for my site and the equations should display properly.
Put Internet Explorer 11 in Compatibility Mode
Look to the right side edge of the Internet Explorer window. You should see a gear icon (it should be right below the "x" icon for closing Internet Explorer). Click on this to open the Tools menu. Down towards the bottom of the Tools menu you should see the option "Compatibility View Settings". Select this option to open a dialog box. In the "Add this website" box Internet Explorer should already have filled in "lamar.edu" for you, if not fill that in. Then all you need to do is click the "Add" button and you will have put the browser in Compatibility View for my site and the equations should display properly.
Can you help me with a problem/homework/
etc
?
Show Answer
Short Answer :
No.
Long Answer :
No.
Long Answer with Explanation :
I'm not trying to be a jerk with the previous two answers but the answer really is "No". Here's why.
My first priority is always to help the students who have paid to be in one of my classes here at Lamar University (that is my job after all!). I also have quite a few duties in my department that keep me quite busy at times. All this means that I just don't have a lot of time to be helping random folks who contact me via this website. I would love to be able to help everyone but the reality is that I just don't have the time. So, because I can't help everyone who contacts me for help I don't answer any of the emails asking for help.
Also, when I first started this site I did try to help as many as I could and quickly found that for a small group of people I was becoming a free tutor and was constantly being barraged with questions and requests for help. Unfortunately there were a small number of those as well that were VERY demanding of my time and generally did not understand that I was not going to be available 24 hours/day, 7 days/week for help. I really got tired of dealing with those kinds of people and that was one of the reasons (along with simply getting busier here at Lamar) that made me decide to quit answering any email asking for help.
So, while I'd like to answer all emails for help, I can't and so I'm sorry to say that all emails requesting help will be ignored.
Where are the answers/solutions to the Assignment Problems?
Show Answer
Answer/solutions to the assignment problems do not exist. Those are intended for use by instructors to assign for homework problems if they want to. Having solutions (and for many instructors even just having the answers) readily available would defeat the purpose of the problems. Please do not email asking for the solutions/answers as you won't get them from me.
How do I download pdf versions of the pages?
Show Answer
There are a variety of ways to download pdf versions of the material on the site.
From Content Page
If you are on a particular content page hover/click on the "Downloads" menu item. You will be presented with a variety of links for pdf files associated with the page you are on. Included in the links will be links for the full Chapter and E-Book of the page you are on (if applicable) as well as links for the Notes, Practice Problems, Solutions to the Practice Problems and Assignment Problems. The links for the page you are on will be
highlighted
so you can easily find them.
From Download Page
All pdfs available for download can be found on the
Download Page
. Links to the download page can be found in the Download Menu, the Misc Links Menu and at the bottom of each page. Once on the Download Page simply select the topic you wish to download pdfs from. This will present you with another menu in which you can select the specific page you wish to download pdfs for. Once you have made a selection from this second menu up to four links (depending on whether or not practice and assignment problems are available for that page) will show up below the second menu that you can click on to initiate the download.
From Site Map Page
The
Site Map Page
for the site will contain a link for every pdf that is available for downloading. You can access the Site Map Page from the Misc Links Menu or from the link at the bottom of every page.
Note for Internet Explorer Users
If you are using Internet Explorer in all likelihood after clicking on a link to initiate a download a gold bar will appear at the bottom of your browser window that will allow you to open the pdf file or save it.
I've found a typo in the material.
Show Answer
If you have found a typo or mistake on a page them please
contact
me and let me know of the typo/mistake. Please be as specific as possible in your report. Let me know what page you are on and just what you feel the typo/mistake is. It's kind of hard to find the potential typo if all you write is "The 2 in problem 1 should be a 3" (and yes I've gotten handful of typo reports like that...).
Some of the equations are too small for me to see!
Show Answer
This is a problem with some of the equations on the site unfortunately. It is especially true for some exponents and occasionally a "double prime" 2nd derivative notation will look like a "single prime". You can click on any equation to get a larger view of the equation. Clicking on the larger equation will make it go away.
If you are a mobile device (especially a phone) then the equations will appear very small. I am attempting to find a way around this but it is a function of the program that I use to convert the source documents to web pages and so I'm somewhat limited in what I can do. I am hoping they update the program in the future to address this. In the mean time you can sometimes get the pages to show larger versions of the equations if you flip your phone into landscape mode.
Another option for many of the "small" equation issues (mobile or otherwise) is to
download
the pdf versions of the pages. These often do not suffer from the same problems.
Is there any way to get a printable version of the solution to a particular Practice Problem?
Show Answer
Yes. If you want a printable version of a single problem solution all you need to do is click on the "[Solution]" link next to the problem to get the solution to show up in the solution pane and then from the "Solution Pane Options" select "Printable Version" and a printable version of that solution will appear in a new tab of your browser.
Calculus I (Practice Problems) / Extras / Proof of Various Integral Properties
[
Notes
]
Calculus I - Practice Problems
Applications of Integrals
Previous Chapter
Proofs of Derivative Applications Facts
Previous Section
Next Section
Area and Volume Formulas
Proof of Various Integral Properties
This section has no problems written yet.
Proofs of Derivative Applications Facts
Previous Section
Next Section
Area and Volume Formulas
Applications of Integrals
Previous Chapter
Calculus I (Practice Problems) / Extras / Proof of Various Integral Properties
[
Notes
]
[
Contact Me
] [
Downloads
] [
Privacy Statement
] [
Site Help
] [
Site Map
] [
Terms of Use
] [
Switch to Mobile View
]
© 2003 - 2018 Paul Dawkins