Mathematics, 10.09.2019 05:20 dshood2298
Find the volume generated by rotating the region bounded by the given curves about the specified line. express the answers in exact form or approximate to the number of decimal places indicated.
find the volume of the solid generated by revolving the region bounded by the curve y = ln x, the x-axis, and the vertical line x=e². about the x-axis. (express the answer in exact form.)
Answers: 1
![\int\limits^{e^2} _{1} \pi {y^2} \, dx \\\\=\int\limits^{e^2} _{1} \pi {(lnx)^2} \, dx \\\pi[x (lnx)^2 -\int\limits^{e^2} _{1} x(2lnx)dx]\\=2(e^1-1)\pi](/tpl/images/0226/5777/00b63.png)
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Find the volume generated by rotating the region bounded by the given curves about the specified lin...
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