We have to find the length of the given curve.

asked 2021-06-01

Find the length of the curve.

\(r(t)=<2t, t^2, \frac{1}{3}t^3>\)

\(0\leq t\leq1\)

\(r(t)=<2t, t^2, \frac{1}{3}t^3>\)

\(0\leq t\leq1\)

asked 2021-08-20

Find the length of the curve.

\(\displaystyle{r}{\left({t}\right)}={\left\langle{6}{t},\ {t}^{{{2}}},\ {\frac{{{1}}}{{{9}}}}{t}^{{{3}}}\right\rangle},\ {0}\leq{t}\leq{1}\)

\(\displaystyle{r}{\left({t}\right)}={\left\langle{6}{t},\ {t}^{{{2}}},\ {\frac{{{1}}}{{{9}}}}{t}^{{{3}}}\right\rangle},\ {0}\leq{t}\leq{1}\)

asked 2021-06-06

Find the length of the curve.

\(r(t)=\langle6t,\ t^{2},\ \frac{1}{9}t^{3}\rangle,\ 0\leq t\leq1\)

\(r(t)=\langle6t,\ t^{2},\ \frac{1}{9}t^{3}\rangle,\ 0\leq t\leq1\)

asked 2021-11-16

Find the length of the curve.

\(\displaystyle{r}{\left({t}\right)}={4}{t},{t}^{{2}},{t}^{{3}},\ {0}\leq{t}\leq{1}\)

\(\displaystyle{r}{\left({t}\right)}={4}{t},{t}^{{2}},{t}^{{3}},\ {0}\leq{t}\leq{1}\)

asked 2021-11-13

Find the length of the curve.

\(\displaystyle{r}{\left({t}\right)}={8}{i}+{t}^{{2}}{j}+{t}^{{3}}{k},\ {0}\leq{t}\leq{1}\)

\(\displaystyle{r}{\left({t}\right)}={8}{i}+{t}^{{2}}{j}+{t}^{{3}}{k},\ {0}\leq{t}\leq{1}\)

asked 2021-09-09

Find the length of the curve. \(\displaystyle{r}{\left({t}\right)}={<}{8}{t},{t}^{{2}},{\frac{{{1}}}{{{12}}}}{t}^{{3}}{>},{0}\leq{t}\leq{1}\)

asked 2021-05-02

Find the length of the curve. \(r(t)=<8t, t^2, \frac{1}{12} t^3> , 0 \leq t \leq 1\)