The volume of the solid obtained by rotating the region bounded by $y = e^x,$ $y = \ln x,$ $x = 1,$ and $x = 2$ about the line $y$-axis can be computed using the method of cylindrical shells. Answer the following questions.

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Using the method of cylindrical shells, set up the integral.

with $a =$ and $b =$

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Find the volume.

Volume =

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