Question

when integrating to find surface area, the usual equations per rotating x-axis or y-axis are the limits of 2(pi)y ds or 2(pi)x ds, however, what about when rotating it around a line eg (x=2) or (y=2)?

Answer 1

In the case of rotating about a line parallel to the x-axis, and therefore using 2(pi)y, you have to adjust the y-value (here, the height of the frustrum used to generate the surface area). So, if you have to rotate about y=2, you would have to adjust your element of surface area as \[2\pi(y-2)ds\]Similarly for rotating about the line x=2, parallel to the y-axis.
Hope it helps.

Answer 2

thanks =)