Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the region under the curve y = √7x from 0 to 28. Solution This problem can be solved using disks. To use shells we relabel the curve y = √7x as x = y shell height = 28-y²/7 y x = y²/7 x = 28 shell radius = y 28 For rotation about the x-axis we see that a typical shell has radius y, circumference 2лy, and height . So the volume is 14 V = S ["¹" (2xY) (28 - 12/1²) dy = (¹^ (28y - 1/1/1³) dy 114 = 2π 2x [ = 0 In this problem the disk method is simpler. 14 y²/7 i dy = 2π

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