]So what I've done is take find the derivative of r wrt θ and use that in the equation for volume,
i.e volume of revolution = $$ \int{2\over 3} r^3 sinθ dθ$$
after substituting $ t=2+3cosθ $ I get $$ \int{2\over 3} {t^3\over-3} dt$$
with the limits from 0 to π in the first case and 5 to -1 in the second case I get the answer as ${104π\over 3}$
Am I doing this right? I feel like there's something really wrong here. Thanks in advance!