I read that proof, and don't care for it.Derive formula of lateral (curved) surface area of cone using integral calculus.
I think those "triangles" are very clumsy to handle.
I would approach it like this . . .We have a right triangle formed by the x-axis, , andCode:| r + * (h,r) | * : | * : | * : - - * - - - - - - - + -- | h
Rotate the triangle about the x-axis to form a cone with radius and height
The surface area is given by: .
So we have: .
. . . . . . .