anonymous
  • anonymous
Let R be the region in the first quadrant bounded by the y-axis, the curve y=sqr(1-x^2)and the line y=xsqr(3). Find the volume of the solid obtained by revolving R about the y-axis.
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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IrishBoy123
  • IrishBoy123
what are you learning with this? looking at it, it is an icecream cone.... which can be done by calculus but it should/could also have other solutions.....especially as it is so symmetrical
anonymous
  • anonymous
yes I was going to use the shell method
IrishBoy123
  • IrishBoy123
There are at least two ways to do it for region |dw:1450138821911:dw|

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anonymous
  • anonymous
yes or discs
IrishBoy123
  • IrishBoy123
|dw:1450140638118:dw| this might be the easiest way to go as you only have 1 integral for the element dx revolved around the y axis, you have area \(dA = \pi (x+dx)^2 - \pi x^2 \approx 2 \pi x dx\). so the volume sitting on that disc is \(dV = 2 \pi x dx (y_2 - y_2) = 2 \pi x dx (\sqrt{1-x^2} - \sqrt{3}x)\) creating integral \(V = 2 \pi\int_0^{1/2} \; dx \; (x\sqrt{1-x^2} - \sqrt{3}x^2)\). going the other way, you need two integrations: |dw:1450140958146:dw| in both cases, the revolved volume of a small element thickness dy about y is \(dV = \pi x^2 dy\) but in region 1 ie \(0
anonymous
  • anonymous
okay, so say I chose to do the disc method
anonymous
  • anonymous
i mean SHELL I WANT TO USE THE SHELL METHOD
IrishBoy123
  • IrishBoy123
this is jargon that i don't ever use, though see quite a lot in these parts. from https://answers.yahoo.com/question/index?qid=20100727183630AAhoIe4 , it seems to me that "shell" is the first one i outlined, and "disc" is the second.
IrishBoy123
  • IrishBoy123
ps i assume it's obvious but will say anyway just in case, but the bottom bit is a cone and you will already know how to do that w/out calculus. have assumed you are practising your skills generally on volumes of revolution. hope this helps in some way
anonymous
  • anonymous
yes, but my question is how to use it

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