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anonymous

  • one year ago

Find the volume using cylindrical shells y = 2ex, y = 2e−x, x = 1; about the y-axis

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  1. myininaya
    • one year ago
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    I like to start with a rough graph first. Is your equations really y=2ex, y=2e-x,x=1?

  2. myininaya
    • one year ago
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    or did you mean y=2e^x,y=2e^(-x),x=1

  3. anonymous
    • one year ago
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    I meant the second one sorry

  4. myininaya
    • one year ago
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    |dw:1436215459219:dw|

  5. myininaya
    • one year ago
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    |dw:1436215629655:dw| so this is the part we want to rotate about the y-axis

  6. myininaya
    • one year ago
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    |dw:1436215740336:dw|

  7. anonymous
    • one year ago
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    ok

  8. myininaya
    • one year ago
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    so since everything is in terms of x you know the y=2e^x and the y=2e^(-x) we are looking at parallel strips to the axis of rotation (like we are already set it up we just have to plug into our formula ) |dw:1436215827622:dw|

  9. myininaya
    • one year ago
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    |dw:1436215907363:dw|

  10. myininaya
    • one year ago
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    are you cool? do you think you can enter into the formula?

  11. myininaya
    • one year ago
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    \[\int\limits_{\text{ lower limit }}^{\text{ upper limit }}2 \pi (Radius)(height) dx\]

  12. myininaya
    • one year ago
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    hint: the height I was trying to show in the picture is just the difference of those two functions

  13. anonymous
    • one year ago
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    yea thank you for the help. So would it have 2 radii

  14. myininaya
    • one year ago
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    radius is x because the distance the curve is from the axis of rotation is x

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