Is this setup correct?
Q: "Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis."
x = 1 + y\(^2\), x = 0, y = 1, y = 3
\[\huge\int\limits_0^{\sqrt{2}} (2 \pi)(y)((3) - (1+y^2)) dy\]
y=3 is the right function
x=1+y\(^2\) is the left function
right - left
Graph below:

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Look good @KingGeorge ? :-)

Wait a minute I'm getting zero when I evaluate...

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