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# Volumes of Revolution watch

1. Question:Find the volume generated when the region bounded by the curve y=x^2, the x-axis and the line x=2, is rotated through 180 degrees about the line x=3.

I've found that the line x=2 and the curve cross at (2,4) so my limits are 4 and 0. How would I form an equation to find the volume using pi ∫ x^2 dy to find the volume? Can x=a even be written as a function of y?

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2. (Original post by Mr Pussyfoot)
Question:Find the volume generated when the region bounded by the curve y=x^2, the x-axis and the line x=2, is rotated through 180 degrees about the line x=3.

I've found that the line x=2 and the curve cross at (2,4) so my limits are 4 and 0. How would I form an equation to find the volume using pi ∫ x^2 dy to find the volume? Can x=a even be written as a function of y?
Since you're rotating about x=3, if you translate the curve then you're rotating about the y-axis. So you need to find things as a function of x, not as a function of y.

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Updated: July 23, 2016
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