Find if and .

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Find

\mathbf{r}(t)

\mathbf{r}'(t) = 2t \mathbf{i} + 3t^2 \mathbf{j} + \sqrt{t} \mathbf{k}

and

\mathbf{r}(1) = \mathbf{i} + \mathbf{j}