Question

#11. Find \overrightarrow{r}(t) if \overrightarrow{r'}(t) = \langle t, e^t, te^t \rangle \\ and \overrightarrow{r}(0) = \hat{i} + \hat{j} + \hat{k}

          #11. Find \overrightarrow{r}(t) if \overrightarrow{r'}(t) = \langle t, e^t, te^t \rangle \\
and \overrightarrow{r}(0) = \hat{i} + \hat{j} + \hat{k}

#11. Find r(t) if r'(t) = ⟨t, e^t, te^t ⟩

and r(0) = î + ĵ + k̂

Added by Deborah B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/20/2023

Step 1

$\overrightarrow{r}(t) = \int \overrightarrow{r'}(t) dt = \int \langle t, e^t, te^t \rangle dt = \langle \frac{t^2}{2}, e^t, e^t(t-1) \rangle + \overrightarrow{C}$ Show more…

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#11. Find $\overrightarrow{r}(t)$ if $\overrightarrow{r'}(t) = \langle t, e^t, te^t \rangle$ and $\overrightarrow{r}(0) = \overrightarrow{i} + \overrightarrow{j} + \overrightarrow{k}$.