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How can I find the length of the curve $$\left(\frac{t^3}{3} - t\right)\mathbf{i}+ t^2 \mathbf{j}, \quad 0≤t≤1?$$

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    When we do the calculation, if we do not make a minor slip, the thing inside the square root turns out, "miraculously," to be a perfect square. Change the numbers a little and you will get something you can't integrate in elementary terms.2012-10-30

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