In this video I go over another example on improper integrals and this time solve the integral of the function sec(x) from x = 0 to x = π/2. This function has a vertical asymptote at x = π/2 because sec(x) approaches infinite as x approaches π/2, thus making it a Type 2 improper integral. Solving this by first writing it as a limit of a definite integral yields a divergent integral because the limit approaches infinite. In this particular integral, the divergent limit represents an infinite area under the curve.
In this video I go over another example on trig substitution for integrals and this time show that sometimes we need to further simplify the integrand to enable trig substitution to be used. In this example I solve the integral of the function x^3/(4*x^2+9)^(3/2) and first complete the square inside the denominator before using trig substitution to solve the integral.
Download the notes in my video: http://1drv.ms/1JI96Ha
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/trigonometric-substitution-for-integrals-example-6
Related Videos:
Trigonometric Substitution for Integrals: Example 6: http://youtu.be/wh2dlrFbxrQ
Trigonometric Substitution for Integrals: Example 5: http://youtu.be/X-35GgXPEHQ
Trigonometric Substitution for Integrals: One to One Function: http://youtu.be/QO26MkCC3eU
Trigonometric Substitution for Integrals: Example 4: http://youtu.be/v3tHdU63Vio
Trigonometric Substitution for Integrals: Example 3: http://youtu.be/Tfl90TqW3jA
The Area of an Ellipse (and Circle): http://youtu.be/7hSkKPQA71s
Trigonometric Substitution for Integrals: Example 1: http://youtu.be/lpp6YLWB2GM
Trigonometric Substitution for Integrals: http://youtu.be/2pWvGXwtVJo
Completing the Square: http://youtu.be/5uxV6-f_qc0
Exact Trigonometry Ratios Part 1: 0, 30, 45, 60, and 90 Degrees: http://youtu.be/ln03a5KvQAY .
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https://www.youtube.com/watch?v=wh2dlrFbxrQ
In this video I go over Question 2 of the Discovery Project: Patterns in Integrals section of my calculus book. In this question I go over the family of integrals of the form with integrand sin(ax)cos(bx) and show how we can derive the general integral formula by finding the pattern that arises from using a computer to quickly solve different examples within that integral family.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIheQwjuYUOlKh5_pw-g
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/discovery-project-patterns-in-integrals-question-2-sin-ax-cos-bx
Related Videos:
Discovery Project: Patterns in Integrals: Question 1: http://youtu.be/uQUu0XFMw8I
Integration using Tables of Integrals: Example 1: http://youtu.be/AOToFP-4Mfg
Can We Integrate All Continuous Functions?: http://youtu.be/OFEDLJYqYps
Integration by Partial Fractions: http://youtu.be/r07NnKf76og
Trigonometry Identities: sin(-x) = - sin(x) and cos(-x) = cos(x): http://youtu.be/tD5EA2SXyFQ
Trigonometry: Product Identities: http://youtu.be/os8XKWAj9P8 .
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https://www.youtube.com/watch?v=O0p1DGMOcfM
A simple explanation of what polynomials are and also how curves of various degrees of polynomials are shown as well as their relative patterns that arise.
Video notes and playlist:
- PDF: https://1drv.ms/b/s!As32ynv0LoaIiv8zPcr3nd8Z4b5IjA
- HIVE: https://peakd.com/hive-128780/@mes/polynomials-simple
- Math basics playlist: https://www.youtube.com/playlist?list=PLE2F47766DE17B783
Related Videos:
Taylor Polynomials - Introduction and Derivation: http://youtu.be/p2EkXwkbflk
Polynomial Long Division - In depth Look on why it works!: http://youtu.be/E1H584xJS_Y
Polynomial Long Division - Examples: http://youtu.be/7XbzCQgqBPc
Factoring Quadratic Polynomials by Guessing: http://youtu.be/biEfGwT5pn4 .
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In this video I go over how to make images transparent in Microsoft Excel. With this method you can actual easily compare an image of a graph with an Excel graph. Make sure you watch this video because this will be very useful at some point in time if you are in school or working in Engineering or other sciences.
Download the notes in my video: https://www.dropbox.com/s/zbuo4awkmdnolpv/326%20-%20Transparent%20Picture%20in%20Excel%20Charts.xlsx
Related Videos:
Convert Time to number, seconds, hours and minutes in Microsoft Excel 2007: http://youtu.be/fwMKbXI98tI
Converting Numbers to Fractions in Microsoft Excel 2007: http://youtu.be/YgJBK0QjIec
Intro to Tables in Excel 2007: http://youtu.be/B_zXmunqrl4
Drop Down Lists with Microsoft Excel 2007: http://youtu.be/e7Sbcn-y9j4
Numbered Headings and Automated Table of Contents - Office Word 2007: http://youtu.be/e00xCQ0MClg
Microsoft Excel Tips: -2^2 = +4 and NOT -4!!!: http://youtu.be/9QC3ZboI3wo
Skip Blanks when Graphing in Microsoft Excel: http://youtu.be/HcCJVUd7a5Q
Automate Formulas using INDIRECT() Function in Excel: http://youtu.be/9WiBtrNq9yU .
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https://www.youtube.com/watch?v=uKjtsQZ5Ow0
In this video my brother, Mark aka MFA, goes through a very simple and basic tutorial on finding the subscriber count of a YouTube Channel that you are subscribed to without unsubscribing. All you have to do is select "About" on the YouTube Channel page and the subscriber count should be there if the channel has made it public.
This may seem very obvious but you would be surprised at how many times I was asked this ;)
Related Videos:
How to fake the amount of YouTube Subscribers with Google Chrome!! ;): http://youtu.be/Jxo23pJApl4
Loop YouTube Videos with InfiniteLooper.com: http://youtu.be/Rnyxs1ntJMw
YouTube Video Manager Bulk Editing and New Line Trick: http://youtu.be/CBOel2oKaPI
YouTube Channel Suspended: How to Get Back on YouTube: http://youtu.be/9EssKZI4FT0 .
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https://www.youtube.com/watch?v=vxYw3ZRUdKo
In this video I illustrate the mean value theorem by going over a useful example which shows how the theorem can be used to find maximum possible values of a function.
Download the notes in my video: http://1drv.ms/NLneZm
Related Videos:
Mean Value Theorem - A Simple Proof: http://youtu.be/x-2MiiG2E38
Mean Value Theorem - Examples: http://youtu.be/qnqURkmj39s
Cauchy's Mean Value Theorem - A simple proof: http://youtu.be/sBW-LwoFWLY
Tangent and Secant Lines: http://youtu.be/9E6fBySBsYw .
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https://www.youtube.com/watch?v=MVa6cj5qOR8
In this video I go over how to disable or to quickly toggle between the shortcut hotkeys on the Windows Surface Pro Tablet PC. Basically I recently got the Surface Pro and was trying to make a Math Easy Solution with it but in order to use the hotkeys for recording the screen using a screen recorder, it is required that the default Microsoft Windows hotkeys be disabled. To do this you can actually use a shortcut hotkey by clicking Fn + Caps Lock. That is all! If you need to make your own hotkeys make sure to watch this video to disable the default Windows 8 hot keys!
Download the notes in my video: http://sdrv.ms/1ab2O5T
Related Videos:
Disable Touch to Click on Trackpad in Microsft 8 Surface Pro Table PC: http://youtu.be/NJSmiKsmMaE
Amazing Google Maps 3D Animation + Gran Fondo Visual Route: http://youtu.be/7otGmGIYO4U
Snapchat Tricks: http://youtu.be/U__a4K22ATM
Replace Samsung S Voice with Google Voice Search on Your Galaxy S4: http://youtu.be/Gcv88jlyQOs
Beware of eBay Sellers Scam: "Can't File Complaint after 30 days...": http://youtu.be/IzKvtUK0nAg
How to Reverse an App Update on your iPhone: http://youtu.be/U7KKb8H4r2E .
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https://www.youtube.com/watch?v=86IW2f40ds0
In this video I go over another example on determining the area of a surface obtained by rotating a curve about an axis. In this example, I calculate the surface area of a shape formed by rotating the arc of the parabola y = x^2 from the point (1, 1) to (2, 4) about the y-axis. As a check of the answer obtained, I calculate the shape of a cylinder as well as a frustum of a cone that is similar to the shape we are trying to calculate, thus the resulting surface areas should all be similar as well.
The solution I use in this video uses the surface area formula in which the arc length is written using dx as opposed to dy. In my next video I solve this same example using dy in the arc length formula instead so stay tuned for that video!
Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103605&authkey=!AMWD5-Q4RS1QsQo&ithint=file%2cpdf
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-surface-area-example-2-solution-1
Related Videos:
Applications of Integrals: Surface Area: Example 1: https://youtu.be/E9rwIVUifuA
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Derivative of y = x^n - Part 2: General Power Rule: http://youtu.be/Ibvu33oh49o
Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8 .
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https://www.youtube.com/watch?v=5nUzb02pDcI
In this video I go over another example on ellipses and this time determine the equation of an inverted ellipse when we are given the foci and vertices.
Download the notes in my video: http://1drv.ms/1MRynRb
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/ellipses-example-2-inverted-ellipse
Related Videos:
Ellipses: Example 1: http://youtu.be/ejhZmTIjiS4
Inverted Ellipses: http://youtu.be/NQQFj66-bxA
Ellipses: Definition and Proof of Equation: http://youtu.be/tvfNgT4CrFs .
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https://www.youtube.com/watch?v=BjddSbZ_AxE