The volume of the solid from the region bounded by $x=9-y^2$, $y=x-7$, $x=0$ about $y=3$ using cylindrical shells.
I've tried creating two separate regions:
$V_1=2\pi(3-y)(9-y^2)dy$ from 3 to 1
$V_2=2\pi(3-y)(y+7)dy$ from 1 to 0
but the answer this gives isn't correct. I can't seem to find any errors in my calculations. Am I devising the solution incorrectly?