I have read and reread the section on the subject of volumes in my calculus book more times than I can remember. When I read it, it makes sense and then when I attempt the problems my integrals and answers do not match the text's. If there is someone out there that can explain what I am missing I would greatly appreciate it!!!!!
For example, there is a cone that is 5 cm tall and has a diameter at the base of 4 cm.
So, I take the integral from 0 to 5 cm of pi times (2 - x)^2 x being the change in the radius as you approach the top of the cone.
I get pi times the integral of 4 + y^2 - 4y dy which has an antidervative of
4y + y^3/3 - 2y^2 and a answer of 35pi/3
My text says the integral should be from 0 to 5 4pi/25 y^2 dy and the volume is 20pi/3 Can someone please tell me why I am incorrect?