Parametric Arc Length Integral Setup

Question

Which of the following integrals gives the arc length of the curve defined by the parametric equations $$x(t)=\ln(t)$$ and $$y(t)=\sqrt{t}$$ for $$t\in [1,e^2]$$?

Accepted Answer

$$\int_{1}^{e^2} \sqrt{\frac{1}{t^2}+\frac{1}{4*t}}\,dt$$

Answer

$$\int_{1}^{e^2} \left(\frac{1}{t}+\frac{1}{2\sqrt{t}}\right)dt$$

Answer

$$\frac{1}{2}\int_{1}^{e^2} \sqrt{\frac{1}{t^2}+\frac{1}{4*t}}\,dt$$

Answer

$$\int_{1}^{e^2} \sqrt{\frac{1}{t}+\frac{1}{4*t}}\,dt$$

Parametric Arc Length Integral Setup

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