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find the volume of the solid that results when the region enclosed by the following...

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user7230927 | Salutatorian

Posted September 20, 2013 at 9:24 PM via web

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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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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted September 21, 2013 at 1:11 AM (Answer #1)

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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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