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Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = -3.

1 Answer

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Using washers, the volume is given by


\displaystyle\pi\int_(x=1)^(x=e)((1+3)^2-(\ln x+3)^2)\,\mathrm dx

=\displaystyle\pi\int_(x=1)^(x=e)(7-6\ln x-(\ln x)^2)\,\mathrm dx
User Serdar Aylanc
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