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Multivariable Calculus

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Arc Length with Parametric Equation

MVCALC-OGXNQJ

Find the arc length of the curve:

$$\vec{r}(t)=(1-\sqrt{2}t)\vec{i}+e^t\vec{j}+(2-e^{-t})\vec{k}$$

...between $\vec{r}(0)$ and $\vec{r}(2)$.

A

$e^2$

B

$e^{-2}$

C

$2e^2$

D

$e^2-e^{-2}$

E

$e^2+e^{-2}$