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$\mathbf{F}=2 y \mathbf{i}+3 x \mathbf{j}+(x+y) \mathbf{k}$ $\mathbf{r}(t)=(\cos t) \mathbf{i}+(\sin t) \mathbf{j}+(t / 6) \mathbf{k}, \quad 0 \leq t \leq 2 \pi$
Step 1
Step 1: First, we differentiate the given vector function $\mathbf{r}(t)=(\cos t) \mathbf{i}+(\sin t) \mathbf{j}+(t / 6) \mathbf{k}$ with respect to $t$ to get $\mathbf{r}'(t)$: \[\mathbf{r}'(t) = -\sin(t)\mathbf{i} + \cos(t)\mathbf{j} + \frac{1}{6}\mathbf{k}\] Show more…
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