Question

Find the volume of a "curved round table" given by rotating the function x=y^2+1 about the y-axis from y=-1 to y=2

Answer 1

what've you tried?

Answer 2

I got Disk method. Integral [-1,2]
(y^2+1)^2 dy

Answer 3

After doing the math I got 126pi/5

Answer 4

ok i'll do it in polar and we can check answers

\(2\pi \int_{z=-1}^{2} \int_{r=0}^{z^2 + 1} r dr dz \)
\(= \pi \int_{-1}^{2} (z^2 + 1)^2 dz \)
\(= \pi \int_{-1}^{2} (z^4 + 2z^2 +1) dz = \dfrac{78\pi}{5}\)

we essentially came out with the same integral but got different numbers

Answer 5

http://www.wolframalpha.com/input/?i=%5Cpi+%5Cint_%7B-1%7D%5E%7B2%7D+%28y%5E2+%2B+1%29%5E2++dy+

Answer 6

this must be calc2 ?

Answer 7

Yea