Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
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nteresting, usually the method of cylindrical shells is used when finding the volume of the solid obtained by rotating about y-axis. Vy = 2pi*[a;b] ∫ x*f(x) dx Bur I suppose that it can be used analogically about x-axis Vx = 2pi*[c;d] ∫ y*g(y) dy Given function is 125y = x^3 -----> x = (125y)^1/3 = 5*y^1/3. Then Vx = 2pi*[0; 8] ∫ y* 5*y^1/3 dy = 10pi * [0; 8] ∫ y^4/3 dy = = 10pi *3/7 * y^7/3 [0; 8] = 30pi/7 * 8^7/3 = 30pi/7 * 2^7 = =30pi/7 *128 = 3840pi/7
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