The discussion revolves around calculating the area and volume related to the function y = x^3, specifically in the context of rotation around the y-axis and the area between two curves. Participants are exploring the definitions and implications of these calculations in a two-dimensional versus three-dimensional context.
The discussion is ongoing, with some participants providing clarifications about the nature of the area in question, emphasizing that it pertains to the xy-plane rather than a three-dimensional surface. There is an acknowledgment of the need to understand the importance of calculating area, though some express uncertainty about its relevance.
Participants are navigating the definitions of area and volume within the constraints of their homework, questioning assumptions about dimensionality and the implications of their calculations.
No, there is no "surface" are because this is not a three dimensional problem. It is simply area in the xy-plane.Miike012 said:When calculating the volume of say y = x^3 rotated around the y-axis from -2<=x<=2 I am the calculating a space occupied by a 3D figure... but when I am calculating the area between say y = x^3 and y=(-x)^3 from 0<= y <=8 what exactly is this area? is it surface area?