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Estudos Gerais • 04/21/2025

Determine o comprimento do arco da curva gerada por

Determine o comprimento do arco da curva gerada por h(x)=12x2+2h(x) = \frac{1}{2}x^2 + 2, para 0≤x≤30 \leq x \leq \sqrt{3}.

A. 22+14ln⁡2\frac{\sqrt{2}}{2} + \frac{1}{4} \ln \sqrt{2} B. 22−ln⁡2\frac{\sqrt{2}}{2} - \ln \sqrt{2} C. 3+12ln⁡(2+3)\sqrt{3} + \frac{1}{2} \ln (2 + \sqrt{3}) D. 32+18ln⁡(2+2)\frac{\sqrt{3}}{2} + \frac{1}{8} \ln (\sqrt{2} + 2) E. 3−12ln⁡(2+3)\sqrt{3} - \frac{1}{2} \ln (2 + \sqrt{3})

Determine o comprimento do arco da curva gerada por \( h(x) = \frac{1}{2}x^2 + 2 \), para \( 0 \leq x \leq \sqrt{3} \). A. \( \frac{\sqrt{2}}{2} + \frac{1}{4} \ln \sqrt{2} \) B. \( \frac{\sqrt{2}}{2} - \ln \sqrt{2} \) C. \( \sqrt{3} + \frac{1}{2} \ln (2 + \sqrt{3}) \) D. \( \frac{\sqrt{3}}{2} + \frac{1}{8} \ln (\sqrt{2} + 2) \) E. \( \sqrt{3} - \frac{1}{2} \ln (2 + \sqrt{3}) \)
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