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8867564

1) Find the volume of the solid of revolution formed when the region bounded between x = 1, x = 4, y = x2 and y = 0 is revolved vertically around the x-axis. Using cans is the answer 21π?

  • one year ago
  • one year ago

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  1. timo86m
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    by x2 you mean x*2 or x^2

    • one year ago
  2. timo86m
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    if x*2

    • one year ago
  3. timo86m
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    |dw:1337145858842:dw| I think

    • one year ago
  4. timo86m
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    area of a small slice will result in a ring so it be pi r2^2 pi r1^2

    • one year ago
  5. colorful
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    I know it as shell method never heard "cans" befor lol

    • one year ago
  6. colorful
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    |dw:1337146309981:dw|we need the height and radius of each cylinder...

    • one year ago
  7. colorful
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    |dw:1337146393852:dw|

    • one year ago
  8. colorful
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    the surface area of a cylinder is given by\[2\pi rh\]so in this case each surface area as a function of x is\[A(x)=2\pi rh=2\pi x^2\cdot x=2\pi x^3\]

    • one year ago
  9. colorful
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    adding up all these areas from x=1 to x=4 should give us the correct integral

    • one year ago
  10. colorful
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    \[V=2\pi\int_{1}^{4}x^3dx\]

    • one year ago
  11. 8867564
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    Thank you for the help on this problem. It was very helpful.

    • one year ago
  12. timo86m
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    deos y=x^2 or x*2?

    • one year ago
  13. 8867564
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    It's x^2

    • one year ago
  14. timo86m
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    oh

    • one year ago
  15. timo86m
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    you can take area from y=0 to y=1 use pi*4^2-pi*1^2=15 pi so that is first part

    • one year ago
  16. timo86m
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    now for 1 to 16 integral(pi*4^2-pi(sqrt(y))^2dy) from 1 to 16

    • one year ago
  17. timo86m
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    I got 127.5000000*Pi

    • one year ago
  18. timo86m
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    let me know what the answer was :)

    • one year ago
  19. marco26
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    what is the answer?

    • one year ago
  20. timo86m
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    I got 127.50*Pi

    • one year ago
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