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Question

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis.

 y=3x^2,  y=18x−6x^2

Answer 1

3x² = 18x - 6x²; x² - 2x = 0; x = 0 or x = 2; v = 2π∫₀²(18x - 9x²)x = 2π(6x³ - 9x⁴/4)₀² = 24π

Answer 2

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