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Math Help - General, basic volume question

  1. #1
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    General, basic volume question

    I'm really confused about this basic volumes question. The question asks: "Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line."

    x = y^2, x = 1; about x = 1

    How do you find the volume if the curve is rotated around a line other than the y or x axis? In this question, but also in general?
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  2. #2
    MHF Contributor
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    Draw the region you are dealing with and then the line of revolution. Seeing it helps set it up I think. When you rotate about lines that aren't the coordinate axis, you just have to account for this when expressing the radius in your integral. Normally the radius is just the function height, so we can just use f(x) or f(y) as our general radius and use the formula. Depending on where the region lies and what line you pick, this can simply add 1 or subtract 1 to the length of each radius. In your problem the line of revolution is also a boundary for the region which makes it easily because if you had a gap (say if you rotated it around x=2) then you have to subtract out this empty space. I think you should look at your textbook or online for a diagram because it's so much clearer to see it.
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