I’m generally very good at math and Calculus this year. I’m in AP Calculus (AB) and have done very well in the class for the most part. But there is one topic I just can not seem to understand no matter what. That topic is The region bounded with Disk, Washer, Shell Methods. It seems no matter how hard I try I just can’t understand that topic. I got a D on the test in class (The worst grade I got on any other test in math this year was an 84%) and when we took a practice test on the released 2012 FRQ’s I scored a 41/54. I’m happy with that but I scored a 1/9 on the Region Bounded one. (I got 2 9’s, 2 8’s and a 6 for the other 5) It doesn’t make sense either because everybody else in my class thinks those problems are the easiest and I just don’t understand them even if try to study them for hours. Does anybody have any advice to fix this?
Intuitively, computing the volume using the disk/washer method is like finding the volume of a bunch (or, infinitely) many thin disks and adding them. You know how to find the volume of a cylinder with base radius r and height h, and it is where the formula comes from.
An easy example: given f(x) = kx from x = 0 to x = h, can you find the volume when f(x) is rotated about the x-axis? (you can easily check if your answer is correct because it should match with the volume of a cone that you learned in geometry or algebra).