1) question asks to find reduction formual for

then it asks hence or otherwise find:

only way i can do this is to do a reduction formula for

What am i missing to be able to use the first result?

2) a surface of revolution is formed by rotating completely about the -axis the arc of

from to

denote by the surface area,show that , the co-ord of the centroid of this surface is given by

3) given area of ellipse is and that the volume generated when this area rotates through about the -axis is

use pappus' theorem to find the centroid.

for this i get the answer but not sure if its ok.

pappus relates to area A enclosed by curve that does not cross -axis,but the ellipse does

"ignoring that"

by pappus,with -coord of centroid

V=Axdistance travelled by G

so

which is correct,but im worried about the crossing x-axis bit.