anonymous
  • anonymous
The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. x = (y − 2)2, x = 1; about y = 1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
This is the graph. The region enclosed has to be rotated around the black line
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anonymous
  • anonymous
Should I use shell or washer on this?
anonymous
  • anonymous
what's the prob? you should be a pro at this now!

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anonymous
  • anonymous
Haha, I know, I always feel confident, set them up, work them out but then when I turn it in, I always get them wrong.
anonymous
  • anonymous
I initially set it up using shell. I had r(y)=y and h(y)=(y-2)^2
anonymous
  • anonymous
r = (y-1) since you're rotating around the line y = 1. limits are 1 to 3. h = (1-(y-2)^2)
anonymous
  • anonymous
Is r = y-1 ?
anonymous
  • anonymous
Ahhh, yes, okay. I had a realization right before you said that, lol
anonymous
  • anonymous
good job!
anonymous
  • anonymous
Yeah. :b But when I worked it out that time I got a negative answer ? 0.0
anonymous
  • anonymous
hold on a sec...|dw:1377645969040:dw| is this what you got for your integral?
anonymous
  • anonymous
Yeah. Then I went from there to\[2\pi \int\limits_{1}^{3}(y-1)(1-(y ^{2}-4y+4))dy\]
anonymous
  • anonymous
that looks right... did you mult out and simplify?
anonymous
  • anonymous
|dw:1377646219115:dw|
anonymous
  • anonymous
which in turn reduces to (y-1)(-y^2+4y-3) and then to 2pi int (from 1 to 3) (-y^3+5y^2-7y+3) dy
anonymous
  • anonymous
|dw:1377646307767:dw|
anonymous
  • anonymous
Yep, that's what I had. When I calculated it all up, I got -184(pi)/12 ):
anonymous
  • anonymous
|dw:1377646494774:dw|
anonymous
  • anonymous
Now, when you do the integration, you plug in the three into the equation, get that result, and then subtract the equation with the one plugged in after, right ?
anonymous
  • anonymous
i get 8pi/3
anonymous
  • anonymous
yes (to your question)
anonymous
  • anonymous
Okay just making sure I didn't do it wrong in that sense. Oooh, okay, I think I see what I did wrong. Messed up a sign.
anonymous
  • anonymous
it happens!

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