The curve y = f (x) in Figure 18, called a tractrix, has the following property: The

Chapter 6, Problem 62

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The curve y = f (x) in Figure 18, called a tractrix, has the following property: The tangent line at each point (x, y) on the curve has slope dy dx = y 1 y2 Let R be the shaded region under the graph of y = f (x) for 0 x a in Figure 18. Compute the volume V of the solid obtained by revolving R around the x-axis in terms of the constant c = f (a). Hint: Use the substitution u = f (x) to show that V = 1 c u 1 u2 du y = f(x) 1 2 y x c R