Question about calculating area and volume

[Miike012]

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?

 

[NascentOxygen]

It's the sum of the areas of all those whisker-thin rectangles, each of height equal to the vertical distance between the curves, viz, x^3 - (-x)^3, and of horizontal width equal to dx or Δx. So it's an area on the x-y plane, a flat area. You could call it a surface area, if you wish, but then all areas could be considered surface areas. couldn't they?

 

[HallsofIvy]

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?

No, there is no "surface" are because this is not a three dimensional problem. It is simply area in the xy-plane.

 

[Miike012]

I guess ill figure out the importance of calculating area later because right now I don't see it..