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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 = -1. (10 points)

Respuesta :

LammettHash
Using the washer method, the volume is given by

[tex]\pi\displaystyle\int_1^e((1+1)^2-(\ln x+1)^2)\,\mathrm dx=\pi\int_1^e(4-(\ln x+1)^2)\,\mathrm dx[/tex]

or by the shell method,

[tex]2\pi\displaystyle\int_0^1(e^y-1)(y+1)\,\mathrm dy[/tex]
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