anonymous
  • anonymous
Which of the following represents the volume of the solid formed by revolving the region bounded by the graphs of y =x^3, y = 1, and x = 2, about the line x = 2?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
https://gyazo.com/a7d6ec10f29833547a39db140db73387
anonymous
  • anonymous
@jim_thompson5910 @zepdrix Appreciate it if you guys could give me a hand.
zepdrix
  • zepdrix
Oh we only have to set it up this time? Nice!

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zepdrix
  • zepdrix
|dw:1444441768757:dw|
zepdrix
  • zepdrix
|dw:1444441990320:dw|Given these boundary lines, do you understand which region we're dealing with?
anonymous
  • anonymous
|dw:1444442057843:dw|
zepdrix
  • zepdrix
Ok good good good. That's the one surrounded by all of our boundaries.
zepdrix
  • zepdrix
OH NOES! :( I just realized.. they have all of the options in terms of y. UGHHHH
zepdrix
  • zepdrix
They set up the integral in terms of y. So we need to actually slice the other direction. Lemme erase all this garbage a sec :c
zepdrix
  • zepdrix
|dw:1444442601942:dw|So instead we'll get a disk :d
anonymous
  • anonymous
I would've never noticed that lol. Good eye
zepdrix
  • zepdrix
\[\large\rm y=x^3\qquad\to\qquad x=y^{1/3}\]Here is how we can think of our curve in terms of y instead of x.
zepdrix
  • zepdrix
|dw:1444442739693:dw|So again, our radius is this blue minus red