a vase is formed by rotating the portion of the curve y^2= x-6 between y=6 and y=-6

Question

anonymous · Answer

about the y axis. Find the volume of the vase

anonymous · Answer

Oops.  Typo, hold on..

anonymous · Answer

This is a disk method problem, which I assume you are familiar with.  The radius of each disk is
x = y^2 + 6
So the area of each disk is pi * (y^2+6)^2  = pi (y^4 + 72y^2 + 36)
and the volume of each infinitesimal slice is pi (y^4 + 72y^2 + 36) dy
Thus we want to evaluate the following integral:
$$V = \pi \int_{-6}^{6} y^4 + 72 y^2 + 36 \space dy = 2\pi \int_0^6 y^4 + 72 y^2 + 36 \space dy$$

anonymous · Answer

Oh damn it i did it again.  that's not 72, it's 12 :)

anonymous · Answer

thank you very much jemurray3!