# What is the arclength of #(t^2-t-1,9t^2-2/t)# on #t in [1,4]#?

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To find the arc length of the curve ( (t^2 - t - 1, \frac{9t^2 - 2}{t}) ) on the interval ( t \in [1, 4] ), you can use the formula for arc length:

[ L = \int_{a}^{b} \sqrt{(dx/dt)^2 + (dy/dt)^2} , dt ]

Substitute the parametric equations for ( x ) and ( y ), and their derivatives with respect to ( t ), into the formula. Then integrate over the given interval ([1, 4]) to find the arc length ( L ).

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