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anonymous

  • one year ago

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?

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  1. anonymous
    • one year ago
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    https://gyazo.com/a7d6ec10f29833547a39db140db73387

  2. anonymous
    • one year ago
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    @jim_thompson5910 @zepdrix Appreciate it if you guys could give me a hand.

  3. zepdrix
    • one year ago
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    Oh we only have to set it up this time? Nice!

  4. zepdrix
    • one year ago
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    |dw:1444441768757:dw|

  5. zepdrix
    • one year ago
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    |dw:1444441990320:dw|Given these boundary lines, do you understand which region we're dealing with?

  6. anonymous
    • one year ago
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    |dw:1444442057843:dw|

  7. zepdrix
    • one year ago
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    Ok good good good. That's the one surrounded by all of our boundaries.

  8. zepdrix
    • one year ago
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    OH NOES! :( I just realized.. they have all of the options in terms of y. UGHHHH

  9. zepdrix
    • one year ago
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    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

  10. zepdrix
    • one year ago
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    |dw:1444442601942:dw|So instead we'll get a disk :d

  11. anonymous
    • one year ago
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    I would've never noticed that lol. Good eye

  12. zepdrix
    • one year ago
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    \[\large\rm y=x^3\qquad\to\qquad x=y^{1/3}\]Here is how we can think of our curve in terms of y instead of x.

  13. zepdrix
    • one year ago
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    |dw:1444442739693:dw|So again, our radius is this blue minus red