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anonymous

  • one year ago

Which integral correctly computes the volume formed when the region bounded by the curves x2 + y2 = 25, x = 3 and y = 0 is rotated around the y-axis? HELP PLEASE

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  1. jtvatsim
    • one year ago
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    Have you sketched it out for yourself? I'm beginning to sketch it for myself right now.

  2. anonymous
    • one year ago
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    yes I have

  3. jtvatsim
    • one year ago
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    From what I'm getting the bounded area is sort of like a pie slice, and the volume looks like a doughnut or something. It's got a big hole through the center.

  4. jtvatsim
    • one year ago
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    |dw:1438138779545:dw|

  5. anonymous
    • one year ago
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    i know the intefral has sqrt 25-y^2 in it

  6. jtvatsim
    • one year ago
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    Yes, that's a good start. We need to take into account the hole as well in order to get the correct integral.

  7. jtvatsim
    • one year ago
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    Our slices are basically "washers" or cylinders with holes. From above, the slices look like this:

  8. jtvatsim
    • one year ago
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    |dw:1438138974699:dw|

  9. jtvatsim
    • one year ago
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    The area of interest is given by taking the big circle area minus the small circle area: \[\pi(\sqrt{25-y^2})^2 - \pi(3)^2\] This gives us \[\pi(14 - y^2)\] when simplified.

  10. anonymous
    • one year ago
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    thank you so much!

  11. jtvatsim
    • one year ago
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    Now for the fun part. Integrating that expression! :)

  12. jtvatsim
    • one year ago
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    We need to integrate from y = 0 to y = 4... do you want to know how I got the y = 4 or did you figure that out?

  13. anonymous
    • one year ago
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    i just needed to know what the integral would be :p

  14. anonymous
    • one year ago
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    yes I did

  15. jtvatsim
    • one year ago
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    Doing the integration for these problems is sort of the "easy" part right? Imagining and drawing them takes patience and practice. :)

  16. jtvatsim
    • one year ago
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    Let me know if you get stuck anywhere on the problem. Good luck!

  17. anonymous
    • one year ago
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    drawing it is where I have the most difficulty but you were much help

  18. jtvatsim
    • one year ago
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    Yep, just keep practicing and trying to draw things. Look up problems with answers online and just practice the drawing part. Don't even integrate. That might be the best way to master these types of problems. :)

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