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
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
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