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Find the volume of the solid that results when the region bounded by the curve x=y² is revolved about the y-axis?

User Flowfree
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Final answer:

To find the volume of the solid formed by revolving the region bounded by the curve x = y² about the y-axis, you can use the method of cylindrical shells.

Step-by-step explanation:

To find the volume of the solid formed by revolving the region bounded by the curve x = y² about the y-axis, we can use the method of cylindrical shells. The volume of each shell is given by 2πy * (x) * dy, where y represents the height of the shell and x represents the radius. In this case, since the curve is x = y², we substitute x with y² in the formula.

The integral to calculate the volume becomes ∫(2πy * (y²) * dy) where the limits of integration are determined by the range of y values that bound the region.

Simplifying the integral and evaluating it will give you the volume of the solid.

User Max Makhrov
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