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anonymous

  • 4 years ago

Rotate the region bounded by the given curves about the given line and find the volume resulting solid. x=1+y^2 and the xaxis from x=1 to x=5 about y=3

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  1. dumbcow
    • 4 years ago
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    |dw:1328507665468:dw| we need the function in terms of x, solving for y y = sqrt(x-1) outer radius(R) = 3 inner radius(r) = 3-sqrt(x-1) \[V = \pi \int\limits_{1}^{5}3^{2} -(3-\sqrt{x-1})^{2} dx\]

  2. anonymous
    • 4 years ago
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    Is this using disk or shell method?

  3. dumbcow
    • 4 years ago
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    disk or washer method

  4. anonymous
    • 4 years ago
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    Do you know how to do it using shell?

  5. dumbcow
    • 4 years ago
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    each vertical cross-section is a ring with outer circle and inner circle

  6. dumbcow
    • 4 years ago
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    i can try...i primarily use the disk method though hold on

  7. anonymous
    • 4 years ago
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    Thanks

  8. dumbcow
    • 4 years ago
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    ok radius = 3-y height = 5-(y^2 +1) = 4-y^2 \[V = 2\pi \int\limits_{0}^{2}(3-y)(4-y^{2}) dy\]

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