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find the volume of the solid formed by rotating the region enclosed by = 11 x=11 y and = 3x=y 3 (with ≥ 0 y≥0) about the y-axis,

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Final answer:

To find the volume of the solid formed by rotating the region enclosed by the curves y = 11x, y = 3x, and x = 0 about the y-axis, use the method of cylindrical shells.

Step-by-step explanation:

To find the volume of the solid formed by rotating the region enclosed by the curves y = 11x, y = 3x, and x = 0 about the y-axis, we need to use the method of cylindrical shells.

The volume of the solid can be found by integrating the volume of each cylindrical shell from 0 to the x-coordinate of the intersection point of the curves.

The radius of each cylindrical shell is the x-coordinate, and the height is the difference between the y-values of the curves. After integrating, the volume can be expressed as V = ∫(2πx(11x-3x))dx.

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