미적 2013 2차 답안

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1. The region between the curve y = sinh−1 x and the x-axis from x = 0 to x = 1 is revolved about the y-axis to generate a solid. Find the volume of the solid. sol’n) The volume of the revolution by Cylindrical shell method

2. Find the center of the mass of the triangular region R with vertices (0,0),(1,0), (0,1) and the density δ(x,y) = xy2. (Hint: let (˜ x, ˜ y) be the center of mass of a typical strip S = {(x,y) ∈R : a ≤ x ≤ a + ∆x}, then y× mass of S = the moment of S with respect to the x-axis).

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