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Fey

  • one year ago

Calculus: The region in the first quadrant bounded by the graphs of the equations y=(1/x), x=1, x=2, is revolved around the x-axis. Use the shell method to find the volume of the resulting solid.

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  1. Fey
    • one year ago
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    I need help finding h(y),,,, (Height)

  2. klimenkov
    • one year ago
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    |dw:1360447641218:dw|

  3. Fey
    • one year ago
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    m,,, ok, I know the bounds are [1,2], the radius is y.... now, the height i want to say (1/y)-1????

  4. klimenkov
    • one year ago
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    \(V=\pi\int \limits_1^2y^2dx\)

  5. Fey
    • one year ago
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    The shell method uses the 2(pi) at the beginning. Can u explain how u got that answere?

  6. klimenkov
    • one year ago
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    Yes. You have to understand what integral means. This solid consists of many little cylinders like on the pic|dw:1360448107971:dw| The volume of the cylinder is \(\pi R^2h\), on the pic \(R\) is \(y(x)\) and \(h\) is \(dx\). We want the whole solid, so we sum the volumes of this small cylinders and get the volume of the solid as an integral.

  7. Fey
    • one year ago
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    well,,, im still not getting the right answere. its suppoased to be (pi)/2....

  8. klimenkov
    • one year ago
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    You have to calculate the integral I wrote correctly.

  9. Fey
    • one year ago
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    Oops. I made a mistake xD Ok, got it thanks.

  10. klimenkov
    • one year ago
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    You are welcome.

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