Let ℜ be the region in the first quadrant bounded by the curves y = x 3 and y = 2 x − x 2 . Calculate the following quantities. (a) The area of ℜ (b) The volume obtained by rotating ℜ about the x -axis (c) The volume obtained by rotating ℜ about the y -axis

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Let ℜ be the region in the first quadrant bounded by the curves y = x 3 and y = 2 x − x 2 . Calculate the following quantities. (a) The area of ℜ (b) The volume obtained by rotating ℜ about the x -axis (c) The volume obtained by rotating ℜ about the y -axis

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Let ℜ be the region in the first quadrant bounded by the curves y = x 3 and y = 2 x − x 2 . Calculate the following quantities.

(a) The area of ℜ

(b) The volume obtained by rotating ℜ about the x -axis

(c) The volume obtained by rotating ℜ about the y -axis

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