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patbatE21

  • 3 years ago

Find the volume generated by revolving about the x-axis the area bounded by xy = 9, the x-axis and lines x = 3 and x=9

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  1. amistre64
    • 3 years ago
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    |dw:1324412465826:dw|

  2. amistre64
    • 3 years ago
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    something similar to this right?

  3. patbatE21
    • 3 years ago
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    Yess

  4. amistre64
    • 3 years ago
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    then we can integrate, or sum up the areas of circles, generated by the function from 3 to 9 i believe

  5. patbatE21
    • 3 years ago
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    May I please see a full work out please?

  6. patbatE21
    • 3 years ago
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    @ amistre64 Alright

  7. amistre64
    • 3 years ago
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    \[\sum_{3}^{4}\pi[f(x)]^2\ \Delta x\] \[\pi \int_{3}^{9}(\frac{9}{x})^2dx\]

  8. amistre64
    • 3 years ago
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    |dw:1324412686951:dw|

  9. amistre64
    • 3 years ago
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    if we take any arbitrary circle created by spinning this about the x axis; we get an area of: pi (y)^2 pi (9/x)^2 the volume generated is then adding up all the circles made from x=3 to x=9

  10. TuringTest
    • 3 years ago
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    are you still stuck? can you not integrate\[\pi\int_{3}^{9}\frac{9^2}{x^2}dx\]? or are you having another problem?

  11. patbatE21
    • 3 years ago
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    @ amistre64 Alright

  12. patbatE21
    • 3 years ago
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    is it 18pi?

  13. amistre64
    • 3 years ago
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    http://www.wolframalpha.com/input/?i=integrate+pi*%289%2Fx%29%5E2+from+3+to+9 18pi looks good to me

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