asked 2021-09-11

Find the Exact length of the curve.

\(\displaystyle{x}={e}^{{t}}+{e}^{{-{t}}},{y}={5}-{2}{t}\) between \(\displaystyle{0}\leq{t}\leq{3}\)

\(\displaystyle{x}={e}^{{t}}+{e}^{{-{t}}},{y}={5}-{2}{t}\) between \(\displaystyle{0}\leq{t}\leq{3}\)

asked 2021-11-19

Find the exact length of the curve.

\(\displaystyle{x}={e}^{{{t}}}+{e}^{{-{t}}},{y}={5}-{2}{t},{0}\le{t}\le{3}\)

\(\displaystyle{x}={e}^{{{t}}}+{e}^{{-{t}}},{y}={5}-{2}{t},{0}\le{t}\le{3}\)

asked 2021-05-02

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

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 2021-09-18

Find the length of the curve.

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

\(\displaystyle{0}\leq{t}\leq{1}\)

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

\(\displaystyle{0}\leq{t}\leq{1}\)

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 2021-09-25

Find the exact length of the curve.

\(\displaystyle{x}=\frac{{1}}{{3}},{\left({y}\right)}^{{\frac{{1}}{{2}}}}{\left({y}-{3}\right)},{1}\leq{y}\leq{9}\)