roadjester
  • roadjester
Find the volume of the resulting solid if the region under the curve y= 1/(x^2+3x+2) from x=0 to x=1 is rotated about (a) the x-axis and (b) the y-axis. (Not bounded by y=0)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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roadjester
  • roadjester
\[1/(x^{2}+3x+2)\]
roadjester
  • roadjester
There are no other restrictions.
TuringTest
  • TuringTest
always nice to have a picture of the area we are looking at|dw:1333301688461:dw|

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TuringTest
  • TuringTest
...something like that ;)
TuringTest
  • TuringTest
around the x axis I recommend disk method are you familiar with it?
roadjester
  • roadjester
It is not bounded by y=0...
roadjester
  • roadjester
Yes, I am familiar with disk, washer, and cyndrilical shells.
TuringTest
  • TuringTest
then it is infinite, hooray!
roadjester
  • roadjester
But only to a certain extent.
roadjester
  • roadjester
That's a good thing?
TuringTest
  • TuringTest
how do you figure? if it is not bounded below by y= something the area is infinite, which means any solid you can get from revolving around a line is infinite, so I'm going to say they mean the positive portion of y.
roadjester
  • roadjester
Huh? So when revolved around the y axis, the answer is infinity?
TuringTest
  • TuringTest
of course if the area is infinite how could the volume obtained by spinning it around something be finite?
roadjester
  • roadjester
Then what about part a: the x-axis?
roadjester
  • roadjester
Mind you, this is an even question so I don't have the answers.
TuringTest
  • TuringTest
if this is the exact wording of the question it is poor it says the area "under the function" but that could be either in the x direction or y direction, so that is lame... I'm pretty sure they mean this region|dw:1333302430100:dw|
roadjester
  • roadjester
but it's not bounded by y=0 like I said. It wasn't in the wording...
TuringTest
  • TuringTest
if it is not this, I have no idea what they mean technically the area \(under\) the graph is infinite if it is this, use disk method to revolve about x
TuringTest
  • TuringTest
...and use shell method to revolve about y
TuringTest
  • TuringTest
I'm quite certain they want you to bound it by y=0, and the challenge to the problem, I believe, is the partial fractions integral that results
roadjester
  • roadjester
Good observation. This question is actually in the section of partial fractions.
TuringTest
  • TuringTest
so do you think you can do it now?
roadjester
  • roadjester
Still working on finding the constants. Quadratics are a pain in the back..
roadjester
  • roadjester
If I use the shell method, what's the radius?
roadjester
  • roadjester
Heck, screw the radius, what are the limits?

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