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anonymous

  • 4 years ago

Integration and volume question: find the volume obtained when the shaded region is rotated through 360 degrees about the y axis.

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  1. anonymous
    • 4 years ago
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    |dw:1328364703100:dw| equation of curve: y= (x+1)^0.5 equation of line: y=x+1 intersection points: (0,1) (-1,0)

  2. dumbcow
    • 4 years ago
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    \[V = \pi \int\limits_{0}^{1}(y^{2}-1)^{2} - (y-1)^{2} dy\]

  3. anonymous
    • 4 years ago
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    how did you get that?

  4. anonymous
    • 4 years ago
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    Revolution solid formule.

  5. anonymous
    • 4 years ago
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    http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithRings.aspx

  6. dumbcow
    • 4 years ago
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    outer radius is x-value of y=sqrt(x+1) --> x = y^2 -1 inner radius is x_value of y = x+1 --> x = y-1

  7. dumbcow
    • 4 years ago
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    horizontal cross-sections are rings with outer and inner radius

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