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:

Question

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:

anonymous · Answer

|dw:1341360986379:dw|

Look good @KingGeorge ?  :-)