Example 3 (a) set up the integral for the length of the arc of the hyperbola xy = 3 from the point (1, 3) to the point 6, 1 2 . (b) use simpson's rule with n = 10 to estimate the arc length. solution (a) we have y = 3 x dy dx = and so the arc length is l = 6 1 + dy dx 2 dx 1 = 6 1 + 9 x4 dx 1 = 6 x4 + 9 x2 dx 1 . (b) using simpson's rule with a = 1, b = 6, n = 10, δx = 0.5, and f(x) = , we have l = 6 1 + 9 x4 dx 1 ≈ δx 3 [f(1) + 4f(1.5) + 2f(2) + 4f(2.5) + ⋯ + 2f(5) + 4f(5.5) + f(6)] ≈ (rounded to four decimal places).