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Work is force x distance, if that's what you need to know. And yes, even with a siphon there is work being done - by the siphon. As for the hose comment, the pipe enters the cylinder from a height one foot above the top. Meaning it has to lift the water 1 extra foot past the top of the cylinder before it can exit.
But before we get too far off topic - let me just say that I figured this out.
I had to take the integral from -1.5 to 1.5 and use 2.5 - x for the height of the pipe for any who was wondering.
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- Artsemis
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There are two keys to being the best:
1.) Never tell everything you know
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