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anonymous

  • one year ago

Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 2, and x = 1 is revolved around the line y = −2.

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  1. anonymous
    • one year ago
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    \[\pi \int\limits_{1}^{e^2} 4 - \ln(x)^2\]

  2. anonymous
    • one year ago
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    okay so in know that, this would be the volume if it was spun around the x- axis just not sure what to do when its revolved around y = -2

  3. anonymous
    • one year ago
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    @ganeshie8 @Hero @jim_thompson5910 any idea ?

  4. jim_thompson5910
    • one year ago
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    |dw:1438914029970:dw|

  5. jim_thompson5910
    • one year ago
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    |dw:1438914089545:dw|

  6. anonymous
    • one year ago
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    yep yep i know what it looks like, i've graphed it

  7. jim_thompson5910
    • one year ago
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    |dw:1438914110494:dw|

  8. jim_thompson5910
    • one year ago
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    you agree it's this region? |dw:1438914141386:dw|

  9. anonymous
    • one year ago
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    yes

  10. jim_thompson5910
    • one year ago
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    we're going to rotate that region around the line y = -2 |dw:1438914218489:dw|

  11. jim_thompson5910
    • one year ago
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    |dw:1438914231869:dw|

  12. jim_thompson5910
    • one year ago
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    |dw:1438914302702:dw|

  13. jim_thompson5910
    • one year ago
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    does that help?

  14. anonymous
    • one year ago
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    it does tell me if this is right

  15. jim_thompson5910
    • one year ago
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    in a sense, you'll have 2 cylinders cylinder A with radius 4 cylinder B with radius ln(x)+2

  16. jim_thompson5910
    • one year ago
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    volume of washer = cylinder A - cylinder B

  17. anonymous
    • one year ago
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    \[\pi \int\limits_{1}^{e^2}16 - (\ln(x) + 2)\]

  18. anonymous
    • one year ago
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    is that right @jim_thompson5910

  19. anonymous
    • one year ago
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    oh woops forgot to square the (ln(x) +2)

  20. jim_thompson5910
    • one year ago
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    \[\Large \pi \int\limits_{1}^{e^2}16 - (\ln(x) + 2)^2\] is correct

  21. anonymous
    • one year ago
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    thank's !!

  22. jim_thompson5910
    • one year ago
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    np

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