Parametric Calculus: Surface Area: Example 1: Sphere

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YouTube Excerpt: In this video I go over an example using the surface area formula for parametric curves, and this time use it to determine the surface area of a sphere with radius r. To do this I first visually show the parametric equations of a circle, and then form a sphere by rotating the top semi-circle about the x-axis. From here I show how we can write the symbolic representation to better memorize the surface area formula, and then after applying the formula, we can then integrate to get the surface area of a sphere, which is 4*pi*r^2. This is a very important video because it shows how we can use parametric curves and equations to determine the relatively famous equation for the surface of a sphere, which adds to the number of ways we can determine a formula. This is a good example in showing that the theorems we create are correct by using them to calculate famous equations, so make sure to watch this video! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuYdoiatwFXg38JXNw View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-calculus-surface-area-example-1-sphere Related Videos: Parametric Calculus: Surface Area Part 3: https://youtu.be/n9vxR0Of7qI Parametric Calculus: Surface Area Part 2: https://youtu.be/Io3tiAUbjRE Parametric Calculus: Surface Area Part 1: https://youtu.be/4bMEIf6WD8M Parametric Calculus: Arc Length Part 1: https://youtu.be/AWvJDK-m6wQ Parametric Calculus: Areas: https://youtu.be/XdplYV61xlM Parametric Calculus: Tangents: https://youtu.be/deQwD2o0Sas Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8 . ------------------------------------------------------ Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over an example using the surface area formula for parametric curves, and this time use it to determine the surface area of a...

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