[SPLIT] Find volume of 16/(x^2+4)-2 rotated about y-axis

The Leonator

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Aug 5, 2007
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I was wondering if someone could please help me with this question. I attempted it but im seriously doubting the quality of my answer.

The graph of y(x) = [16/(x^2 +4)] -2 from -2≤x≤2 Is rotated about the y-axis to form a upsidown, bowl like shape (filled). Calculate the volume.

I know that i have to use the formula: V= ∏∫[([16/(x^2 +4)] -2)^2]dx evaluated from -2 to 2 but im pretty sure I have evaluated it wrong.

Thank you.

-Leonator
 
I'm sure someone will be glad to check your work and answer, but you'll need to post them first. :oops:

Please be specific. Thank you! :D

Eliz.
 
The Leonator said:
I know that i have to use the formula: V= ∏∫[([16/(x^2 +4)] -2)^2]dx evaluated from -2 to 2 but im pretty sure I have evaluated it wrong.
I've often wondered the point of knowing you did something wrong. Why not try it again until you get it?

I'll give you a hint. Your function is symmetric about the y-axis. If your limits are [-2,2], you'll fill the whole thing twice. You may wish to stick with [0,2].

Another hint. Since you are thinking [-2,2], you must be integrating along the x-axis. That would make little sense for disks perpendicular to the y-axis.

Let's see what you get on your second try.
 
Remember, when using shells, the cross-sections are parallel to the axis about which it's being revolved. Therefore, they'll be
'stacked up'along the x-axis.

Sorry, but the LaTex has been down for several days now. I forgot.

rotate12ms4.gif
 
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