amonoconnor
  • amonoconnor
Would someone be willing to check my answer for the following problem involving volumes of solids? y = 2/(x^1/2), y = 2, x = 4; about the x-axis. Any and all help is greatly appreciated! :)
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
so basically
anonymous
  • anonymous
\[y=\frac{ 2 }{ \frac{ x }{ 2 } }\]
anonymous
  • anonymous
so y =\[\frac{ 4 }{ x }\]

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amonoconnor
  • amonoconnor
No... one of the equations defining the area to be revolved is y = 2/(x^(1/2)) and another serving as a limit, and boundary value for the integral, is y = 2.
AccessDenied
  • AccessDenied
We might start with a sketch of our situation. This one is pretty tough to visualize, so a graphing calculator might help if that is available. Here is Wolfram's plot: http://www.wolframalpha.com/input/?i=plot+y%3D2%2Fx%5E%281%2F2%29%2C+y%3D2%2C+x%3D4 You want to revolve this region about the x-axis. First, did you have any ideas on how you might set this one up? :)
AccessDenied
  • AccessDenied
Since the region is not connected to the x-axis, I think the washer method is looking good here. We need to figure out the limits, and then decide what our inner and outer radius are. If you need more help, I can return to this if you reply soon (I just saw you are offline), or just bump it and someone else can help. Good luck!
amonoconnor
  • amonoconnor
Sorry, my iPad does show me as inactive in OS even when I'm not some times... Annoying :p Anyways, yes, I used the Washer Method. I determined... (And please tell me if any of this is incorrect) Boundaries: since we are revolving around the x-axis, they are x-values of: 1, 4. R: 2 r: (2/(x^(1/2))
AccessDenied
  • AccessDenied
I agree with that information, yes. :)
amonoconnor
  • amonoconnor
After taking the anti-derivative, but before plugging in the boundaries to solve, I had: "pi(4x - 4(ln(x))) 1|4" ?
AccessDenied
  • AccessDenied
Looks good!
amonoconnor
  • amonoconnor
Sweeeet! :)
amonoconnor
  • amonoconnor
And... For a final answer, I am getting "4pi(4 - ln(4))" ??
amonoconnor
  • amonoconnor
*units cubed
AccessDenied
  • AccessDenied
Looks like something was lost. What was the steps after you plugged in your limits of integration?
amonoconnor
  • amonoconnor
What I have on my paper: = pi(4x - 4(ln(x))) 1|4 = [pi(4(4) - 4(ln(4)))] - [pi(4(1) - 4(ln(1)))] = [pi(16 - 4(ln4))] - [pi(4 - 0)] = 16pi - 4pi(ln4) - 4pi = 4pi(4 - ln(4)) units^3
amonoconnor
  • amonoconnor
Oh!!! I think I se a mistake... Is it that I didn't subtract 4pi from 16pi, so to should be: 4pi(3 - ln(4))
AccessDenied
  • AccessDenied
Yep, there you go! I was thinking either that or you made the other x=1 limit all 0 (just because ln 1 = 0). But that fixes it! :D
amonoconnor
  • amonoconnor
Alright, sweet, so the final answer is indeed 4pi(3 - ln(4)) ? :D
AccessDenied
  • AccessDenied
That's what I got as well.
amonoconnor
  • amonoconnor
Awesome! Thank you very much for your patience and willingness to work with me! It helped, and I fully understand what went wrong, I'm not just confused. Thank you!
AccessDenied
  • AccessDenied
Always glad to help! :D

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