Question

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Calcule o comprimento da curva α(t)=(2t,√5t), t∈[2,3]

Answer 1

$\displaystyle L=\int_{2}^3\sqrt{\left[\frac{d}{dt}(2t)\right]^2+\left[\frac{d}{dt}(\sqrt5t)\right]^2} dt\\ \\ L=\int_{2}^3\sqrt{2^2+\sqrt5^2} dt\\ \\ L=\int_{2}^3\sqrt{9} dt\\ \\ L=3\int_{2}^3 dt\\ \\ \\ \boxed{L=3}$