i have now sorted out questions 1 and 3.
2 still eludes me. I can not get the t^3 in the integral and cant see why we have a 3 as the upper limit for the integral and not rt(3)
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.