Find the arclength of the curve \mathbf r(t = \langle 6 t^2, 2\sqrt{6} t, \ln t\rangle, 1 \le t \le 4

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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