At first, I kept the problem in terms y and used 1 and 3 as the bounds. I also tried putting it in terms of x and found that the second bound was 6 and the first bound was given which was 0. I'm confused about how to determine the bounds. How does the given information, $\ x=6+y^2, x=0, y=1,$ and $\ y=3$ , help us solve the problem?
2026-04-08 00:48:27.1775609307
Find the volume of the solid obtained by rotating the region bounded by the curves $\ x = 6+y^2, x=0, y=1$, and $\ y = 3 $ about the x-axis.
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Integrating with respect to $y$ and using 1 and 3 as your bounds makes a lot of sense.
Sketch the region if you are having trouble finding your bounds. Here is my sketch of your region.
If you wanted to integrate with respect to x, you would need to break this into two integrals. One from 0 to 7 and one from 7 to 15.