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WZ
Numerade Educator

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Problem 65 Hard Difficulty

Calculate the volume generated by rotating the region bounded by the curves $ y = \ln x $, $ y = 0 $ and $ x = 2 $ about each axis.
(a) The y-axis
(b) The x-axis

Answer

a) $\pi\left(4 \ln 2-\frac{3}{2}\right)$
b) $\pi\left[2(\ln 2)^{2}-4 \ln 2+2\right]=2 \pi\left[(\ln 2)^{2}-2 \ln 2+1\right]$

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Video Transcript

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