Loading [MathJax]/jax/output/HTML-CSS/fonts/TeX/fontdata.js
Note. In each example, the illustration shows the space curve. The part of the curve highlighted in red is the part whose length you are asked to find.
Find the length of \definecolor{answer}{RGB}{0,0,200}\mathbf{r}(t) = \langle \cos t, \sin t, t \rangle from t=-2 to t=2.
Find the length of \mathbf{v}(t) = \langle 12t,8t^{3/2},3t^2 \rangle from t=0 to t=1.
Find the length of \mathbf{r}(\theta) = \cos^3\theta\,\mathbf{i} + \sin^3\theta\,\mathbf{j} from \theta=0 to \theta=2\pi.
Find the length of \mathbf{r}(u) = \langle 1,-u^2,u^3 \rangle from u=0 to u=1.