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anonymous

  • 5 years ago

Determine the volume of the solid obtained by rotating the portion of the region bounded by and that lies in the first quadrant about the y-axis.

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  1. amistre64
    • 5 years ago
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    your trying to tempt me arent ya :)

  2. anonymous
    • 5 years ago
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    Nope. Not in the least. ;)

  3. amistre64
    • 5 years ago
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    is this saying the volume of the first quadrant spun around the y axis?

  4. anonymous
    • 5 years ago
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    Yup. Which is to say, bound by both axis with the limits being each intersection

  5. amistre64
    • 5 years ago
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    i appear to be missing a function to determine proper bound lol; or have gone blind :)

  6. anonymous
    • 5 years ago
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    Oh you're right they didn't post... My bad! It's y=(x^1/3) and y =x/4

  7. amistre64
    • 5 years ago
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    x^3 = x/4 would be the bounds then right...

  8. amistre64
    • 5 years ago
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    cbrt(x)=x/4 typoed it lol

  9. amistre64
    • 5 years ago
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    im going with 0 to 4

  10. amistre64
    • 5 years ago
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    gotta redo that lol

  11. amistre64
    • 5 years ago
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    0 to 8 ...

  12. anonymous
    • 5 years ago
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    Yeah try again lol

  13. anonymous
    • 5 years ago
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    There you go

  14. amistre64
    • 5 years ago
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    my stupidity got in the way

  15. anonymous
    • 5 years ago
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    I forgive you. 64 is awfully close to one. ;)

  16. amistre64
    • 5 years ago
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    spin around the y axis....

  17. amistre64
    • 5 years ago
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    we can do this from 0 to 2 on the y right

  18. anonymous
    • 5 years ago
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    Less bored?

  19. myininaya
    • 5 years ago
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    lol nerds!

  20. amistre64
    • 5 years ago
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    less.... :)

  21. anonymous
    • 5 years ago
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    Yes, if you mean in terms of y.

  22. amistre64
    • 5 years ago
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    one radius is x=4y the other is .....

  23. amistre64
    • 5 years ago
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    y^3?

  24. anonymous
    • 5 years ago
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    I wouldn't do it that way.

  25. amistre64
    • 5 years ago
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    \[\pi \int\limits_{0}^{2} [4y]^2 - [y^3]^2 dy\]

  26. anonymous
    • 5 years ago
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    Though yes. You can. The top one being?

  27. amistre64
    • 5 years ago
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    why is it gonna break?

  28. anonymous
    • 5 years ago
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    Haha no,but yeah that's right. Let's pretend y just put inthe calculator and got it right because you can push buttons well. :)

  29. amistre64
    • 5 years ago
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    i get 128/3 - 128/7

  30. amistre64
    • 5 years ago
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    512/21 = 24.381 ??

  31. amistre64
    • 5 years ago
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    if I do shelss; i wonder if i get the same result :)

  32. anonymous
    • 5 years ago
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    That was fun :) it's 512 pi/21you forgot pi lol

  33. amistre64
    • 5 years ago
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    i think i dropped a pi lol

  34. amistre64
    • 5 years ago
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    ack!!.... yeah, just realized it :)

  35. amistre64
    • 5 years ago
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    76.59 closer?

  36. amistre64
    • 5 years ago
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    yes!! shell and disk are the same yay!!

  37. amistre64
    • 5 years ago
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    \[2\pi \int\limits_{0}^{8} x(x^{4/3}) -x(\frac{x}{4}) dx\] = 76.59

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