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

Thus, we have an arc length of:

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To find the arc length of the curve ( (t^2 \ln t, t - \ln t) ) on the interval ([1, 2]), you can use the formula for arc length:

[ L = \int_{a}^{b} \sqrt{[f'(t)]^2 + [g'(t)]^2} , dt ]

where ( f(t) ) and ( g(t) ) are the parametric equations defining the curve. Calculate the derivatives of ( f(t) ) and ( g(t) ), then plug them into the formula and evaluate the integral over the interval ([1, 2]).

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