(All Steps) (a) (3 points) Find the arc length of the curve parametrized by r(t)=3 cos (t) i+3 sin (t) k+4 t k, 0 ≤q t ≤q 2 π (b) (5 points) For
Question: (a) (3 points) Find the arc length of the curve parametrized by \(\mathbf{r}(t)=3 \cos (t) \mathbf{i}+3 \sin (t) \mathbf{k}+4 t \mathbf{k}\), \(0 \leq t \leq 2 \pi\)
(b) (5 points) For \(\mathbf{F}=y x^{3} \mathbf{i}+y^{2} \mathbf{j}\), find \(\int_{C} \mathbf{F} \cdot d \mathbf{r}\) on the portion of the curve \(y=x^{2}\) from \((0,0)\) to \((1,1)\)
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![[Solution Library] Consider the region \mathcalR enclosed](/images/solutions/MC-solution-library-71881.jpg "[Solution Library] Consider the region \mathcalR enclosed by the")
[Solution Library] Consider the region \mathcalR enclosed by the
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