In this video I revisit my earlier proof of the area of a sector of a circle, and this time show how it can be solved using only definite integrals. In my earlier proof video I used an indefinite integral method to solve the step that involved trig substitution for integrals because I did not want to change the intervals of integration. But in this video using only definite integrals provides a useful concept to understand, which is always keeping track of the variables being used or substituted. Thus by using the definite integral method, I show how the angle I am substituting is different than the actual angle of the sector of the circle that I am deriving the area for. This is a pretty interesting and useful video on understanding the importance of the intervals of integration so make sure to watch this video!
Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104271&authkey=!AND6pxQG88tEyDo&ithint=file%2cpdf
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/area-of-a-sector-of-a-circle-revisited-using-definite-integrals-only
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I don't always determine the area of a sector of a circle but when I do I usually revisit it to solve it using only definite integrals ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/area-of-a-sector-of-a-circle-revisited-using-definite-integrals-only