Parametric Calculus: Surface Area Part 3

Math Easy Solutions

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In this video I go over Part 3 of the surface area for parametric curves videos series, and this time extend the formula derived in Parts 1 and 2 even further. The formula derived was for determining the surface area of a shape formed by rotating the parametric curve about the x-axis, but in this video I show that it is in fact similar for if it’s rotated about the y-axis. The only thing that changes is the “radius” of a segment being rotated becomes “x” as opposed to “y”. I also I show that the symbolic representation of the surface area is the same as that for surface area of a regular function, and similar to the arc length formula, which I have covered in earlier videos. Basically we can replace the arc length segment thickness with “ds”. I show the visual representation of this term and corresponding formulas for the shapes formed by rotating by the x and y-axis. This is a great video to get a better understanding of just how the surface area formula is visually represented which helps in memorizing how to apply this formula, so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuYFyjD5wqpw7PVL_g

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-calculus-surface-area-part-3

Related Videos:

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 3 (Debunking My Own Video): https://youtu.be/udz4jzUgPBg Parametric Calculus: Arc Length Part 2: https://youtu.be/anD_j0nDDPA 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 .