We’ve reached trimester 3! Last week we took the tri 2 exam, and I am super glad to be done with that trimester. We started this trimester by continuing to learn about the various methods that are used to find the area of a graph rotated around an axis. The shell method was the main idea this week, and I think this is my favorite one so far. It seems to be the easiest. It is pretty similar to the washer method, except it has a few minor changes to the formula. With the shell method, you multiply the integral by 2pi which is different than previous formulas, and you multiply the function by x, which represents the distance from the origin to the center of rotation. With previous methods we had to square parts of the function or things like that, so just multiplying by x makes the shell method the easiest in my opinion. It still shares the same idea of rotating things around an axis and finding their area or volume, but takes fewer steps. Both the worksheet and the assignment went well for me when working with this method, so hopefully things continue that way. I feel like I understand all of the methods fairly well, but my fear is that I will confuse them and all of their different parts when it comes to being tested on it. That is something that I will definitely have to work on.
https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/shell-method/v/shell-method-for-rotating-around-vertical-line
https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/shell-method/v/shell-method-for-rotating-around-vertical-line