find the volume of the solid that results when the region enclosed by the following constraints are revolved about the x-axis. `y=e^x`   , `y=0`   ,  `x=0`   , `x=ln2`

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The volume can be found using the disk method:

`V=pi int_(a)^(b)[R_x]^2 dx` where `R_x` is the height of the representative element.

`V=pi int_0^(ln2) [e^x]^2 dx`

`=pi int_0^(ln2) e^(2x)dx`   

`=pi/2 int_0^(ln2) 2e^(2x)dx`

`=pi/2[e^(2x)|_0^(ln2)]`

`=pi/2[e^(2ln2)-e^0]`

`=pi/2[e^(ln4)-1]`

`=(3pi)/2`

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The volume is `(3pi)/2` cubic units

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