Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Buy my book!: '1001 Calculus Problems for Dummies' - you can get it on my website: http://patrickjmt.com/ Practice Problems with Detailed Solutions made by me! : http://www.teacherspayteachers.com/Product/Calculus-Volumes-of-Revolution Volumes of Revolution - Disk/Washers Example 1. A problem is shown about how to use the disk/washer method to find a volume of revolution about the X axis.
Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Problems with Detailed solutions made by me! : http://www.teacherspayteachers.com/Product/Calculus-Volumes-of-Revolution In this video, I use the same region from part 1, but now I rotate the region about the line y = - 2. For more free math videos, visit http://PatrickJMT.com
Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Longer Version - Volumes using Disks/Washers - In this video I do numerous examples of calculating volumes or regions using the disk/washer method. For more free math videos, visit http://PatrickJMT.com
Media outlets around the world went crazy over a 5th grade math exam question in China. But they all missed the real story! The problem actually dates back to French researchers in 1979. In this video I present the real story to the viral "Chinese" captain's age question. Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Update thanks to comment from Markus Schüt: the origin dates back to 1841 in a letter Flaubert wrote! See: https://en.wikipedia.org/wiki/Age_of_the_captain My blog post for this video: https://wp.me/p6aMk-5rE Captain's age question "If a ship had 26 sheep and 10 goats onboard, how old is the ship's captain?" South China Morning Post http://www.scmp.com/news/china/society/article/2130892/26-sheep-10-goats-lot-flak-over-chinese-primary-school-maths-exam The Portal (Chinese) http://www.thepaper.cn/newsDetail_forward_1971117 RT https://www.rt.com/news/417231-china-math-problem-sheep-goats/ BBC http://www.bbc.com/news/world-asia-china-42857864 Washington Post https://www.washingtonpost.com/news/worldviews/wp/2018/01/31/this-chinese-math-problem-has-no-answer-actually-it-has-a-lot-of-them/ Newsweek http://www.newsweek.com/can-you-solve-it-bizarre-math-exam-question-leaves-students-scratching-their-796005 Official response (Chinese). http://news.sina.com.cn/s/wh/2018-01-27/doc-ifyqzcxh0729685.shtml Sherlock Holmes' deduction in The Hound of the Baskervilles https://www.quora.com/What-are-some-of-the-best-deductions-by-Sherlock-Holmes Novotná, Jarmila, and Bernard Sarrazy. "Model of a professor’s didactical action in mathematics education: professor’s variability and students’ algorithmic flexibility in solving arithmetical problems." The Fourth Congress of the European Society in Mathematics Education. 2005. http://www.erme.tu-dortmund.de/~erme/CERME4/CERME4_WG6.pdf#page=68 de Corte, Eric, Brian Greer, and Lieven Verschaffel, eds. Making Sense of Word Problems. CRC Press, 2000. Pages 3-5. https://books.google.com/books?id=OOyHRpWsI7sC&lpg=PR7&ots=oRk2XlgRGu&dq=%2226%20sheep%22%20%2210%20goats%22%20boat&lr&pg=PA4#v=onepage&q=%2226%20sheep%22%20%2210%20goats%22%20boat&f=false Reusser, Kurt. "Problem solving beyond the logic of things: Contextual effects on understanding and solving word problems." Instructional Science. 17.4 (1988): 309-338. https://files.eric.ed.gov/fulltext/ED270327.pdf Benjamin Dickman Twitter and tweet https://twitter.com/benjamindickman/status/960304080462798851 Benjamin Dickman answer on Math Educators Stack Exchange https://matheducators.stackexchange.com/questions/11543/does-the-how-old-is-the-shepherd-phenomenon-occur-for-more-relatable-word-prob/11546#11546 Gene Wirchenko blog http://genew.ca/solving-the-right-problem-right/ If you like my videos, you can support me at Patreon: https://www.patreon.com/mindyourdecisions Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you. My Blog: https://mindyourdecisions.com/blog/ Twitter: https://twitter.com/preshtalwalkar Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965 Google+: https://plus.google.com/108336608566588374147/posts Pinterest: https://www.pinterest.com/preshtalwalkar/ Tumblr: https://preshtalwalkar.tumblr.com/ Instagram: https://instagram.com/preshtalwalkar/ Patreon: https://www.patreon.com/mindyourdecisions Newsletter (sent only for big news, like a new book release): http://eepurl.com/KvS0r If you buy from the links below I may receive a commission for sales. This has no effect on the price for you. My Books "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.8/5 stars on 31 reviews) http://amzn.to/1uQvA20 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias". (rated 4.6/5 stars on 3 reviews) http://amzn.to/1o3FaAg "Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews. http://amzn.to/1GhUUSH "Math Puzzles Volume 2". (rated 4.3/5 stars on 4 reviews) http://amzn.to/1NKbyCs "Math Puzzles Volume 3". (rated 3.8/5 stars on 5 reviews) http://amzn.to/1NKbGlp "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews) http://amzn.to/1LOCI4U "The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 4 reviews) http://amzn.to/18maAdo "Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews) http://amzn.to/XRm7M4
In this video we find the volume of the solid obtained by rotating a region bounded by y=e^(-x), y=1, and x=2 about the horizontal line y=1. To do so, we use the disk method horizontal axis of rotation formula. Disk Method, Horizontal Axis of Revolution
Sample problems and introduction
Finding the solid of revolution (constructed by revolving around the x-axis) using the disc method. Created by Sal Khan. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-definite-integrals/ab-disk-method/e/the-disk-method?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-definite-integrals/ab-disk-method/v/generalizing-disc-method-around-x-axis?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-definite-integrals/ab-horizontal-area/v/area-between-two-functions-of-y?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago. About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
Introduction on how to understand the theory and principle on areas bounded by a curve and volumes of solids of revolutions.
► My Applications of Integrals course: https://www.kristakingmath.com/applications-of-integrals-course Learn how to find the volume of rotation around a line defined for x in terms of y. Volume of rotation problems are essentially area between curves problems but with a slightly different formula that accounts for the 3D component. ● ● ● GET EXTRA HELP ● ● ● If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com ● ● ● CONNECT WITH KRISTA ● ● ● Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;) Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!” So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com FACEBOOK // https://www.facebook.com/KristaKingMath TWITTER // https://twitter.com/KristaKingMath INSTAGRAM // https://www.instagram.com/kristakingmath/ PINTEREST // https://www.pinterest.com/KristaKingMath/ GOOGLE+ // https://plus.google.com/+Integralcalc/ QUORA // https://www.quora.com/profile/Krista-King
Ms. Roshan's AP Calculus AB Videos -- Based on Stewart's Calculus: Concepts & Contexts * Understand the definition of volume, as both a limit and an integral * Prove the equation for volume of a sphere * Calculate volumes of revolution, using the disks method and washers method * Calculate volumes using cross-sections Animations via: http://mathdemos.org/mathdemos/diskmethod/diskmethodgallery.html https://www.youtube.com/watch?v=3oAjcLD34kc https://www.youtube.com/watch?v=mQj0w8nVyc4