Polar Coordinates: Area Formula скачать в хорошем качестве

Polar Coordinates: Area Formula

In this video I go over further into Polar Coordinates and this derive the formula for determining the area of a polar curve. In doing this I make note of the formula for the area of a sector of a circle which I covered in my earlier video, and is equal to ½r2ϴ. Then just like in deriving the formula for the area under a curve in basic Cartesian coordinates, we divide the region into many parts, but the only difference now is that split the angle into many subintervals of equal angle Δϴ. Now instead of summing up an infinite amount of infinitely small rectangles, we instead sum up sectors of a circle. Then we can write the summation as a limit as the intervals approach infinity, which when we consider it as a Riemann Sum we get the formula for the area of the polar curve. Note though that the summation I derived is not exactly as the Riemann Sum formulas I derived in my earlier videos, because now we are dealing with a squared function, this is in fact still the case and which I may prove in a later video so stay tuned! This is a very useful video to understand how to derive the formula for the area of a polar curve which I will be utilizing in my later videos, and also a good way to compare with the Cartesian area derivation, so make sure to watch this video! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvUPW... View video notes on the Hive blockchain: https://peakd.com/@mes/video-notes-po... Related Videos: Polar Coordinates: Graphing With Polar Curves with Desmos Calculator:    • Polar Coordinates: Graphing With Polar Cur...   Polar Coordinates: Cartesian Connection:    • Polar Coordinates: Cartesian Connection   Polar Coordinates:    • Polar Coordinates   Parametric Equations and Polar Coordinates:    • Parametric Equations and Polar Coordinates   Area of a Sector of a Circle: Proof:    • Area of a Sector of a Circle: Proof   Equation of a Circle and it's proof:    • Equation of a Circle - and its Proof   Integration Overview: How are Riemann Sums, Antiderivatives, and Integrals Linked?:    • Integration Overview: How are Riemann Sums...   . ------------------------------------------------------ Become a MES Super Fan!    / @mes   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: [email protected] 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