Consider the region bounded by y = x² and y = 3x. Each integral below gives the volume generated by rotating this region about some axis. Identify the axis of rotation for each integral. Hint: You may use some answers more than once. 3/² = ((3x)² - (x²) ²) dx ~S = ( ( 3x + 9)²³ - (x² + 9) ²) dx L² = ((9-x²)² - (9- 3x)²) dx [ 2x [² 2xy ( √5 - 1) dy S² = ( ( √² ) ² - ( ² ) ²) dy ~S² = ( ( 9 - ²)²³ - (9 - √5)²) dy x-axis y-axis ✓ X=9 X=-9 y=9 y=-9 y-axis x-axis ✓ 2л (9 − x) (3x − x²) dx ²2 (y + 9) (√5 - 1) dy

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