Repeat Exercise 1 with the parametrization \(\mathbf{r}(t)=\left\langle 3 t^{2}, t^{2}, t^{2}ightangle\) for \(0 \leq t \leq \sqrt{2}\).

Data From Exercise 1

Let \(f(x, y, z)=x+y z\), and let \(C\) be the line segment from \(P=(0,0,0)\) to \((6,2,2)\).

(a) Calculate \(f(\mathbf{r}(t))\) and \(d s=\left\|\mathbf{r}^{\prime}(t)ight\| d t\) for the parametrization \(\mathbf{r}(t)=\langle 6 t, 2 t, 2 tangle\) for \(0 \leq t \leq 1\).

(b) Evaluate \(\int_{C} f(x, y, z) d s\).