# How do you find the volume of the solid generated by revolving the region bounded by the curves y = 2x and y = x² rotated about the y-axis?

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To find the volume of the solid generated by revolving the region bounded by the curves (y = 2x) and (y = x^2) rotated about the y-axis, you can use the method of cylindrical shells. First, determine the bounds of integration by finding the points where the two curves intersect. Then, express the volume element of a cylindrical shell as (2\pi rh), where (r) is the distance from the axis of rotation to the shell, and (h) is the height of the shell. Integrate this expression with respect to (y) from the lower bound to the upper bound. Finally, evaluate the integral to find the volume of the solid.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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