(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the volume of the solid of revolution of the area bounded by the curves about the given axis.

y= x^2 - 2, y = 0, about y = -1, consider only the area above y=-1

2. Relevant equations

3. The attempt at a solution

So I drew out the problem and figured it would be simplest to use a double integral. I'm not sure how to write this nicely but, I got:

4pi * (integral from -1 to 0 of y(integral from 0 to sqrt(y+2) of dx) dy)

Hopefully you can read that. Note I cut it in half so I multiply by 2 to get the volume I want. I'm fairly positive this is right, I'm just curious as to why i am getting a negative answer. If I just have to switch the integral from (-1 to 0) to (0 to -1) why is that? or did I set the problem up wrong since the axis is y=-1?

Also is there a simple way to cover the problem with a single single intgral (I know i can break it up)?

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# How to set up double integral for volume by rotation

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