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Problem 45 Easy Difficulty

Use a CAS to perform the following steps to evaluate the line integrals.
a. Find $d s=|\mathbf{v}(t)|$ d $t$ for the path $\mathbf{r}(t)=g(t) \mathbf{i}+h(t) \mathbf{j}+k(t) \mathbf{k}$.
b. Express the integrand $f(g(t), h(t), k(t))|\mathbf{v}(t)|$ as a function of the parameter $t$.
c. Evaluate $\int_{C} f d s$ using Equation (2) in the text.
$f(x, y, z)=x \sqrt{y}-3 z^{2} ; \quad \mathbf{r}(t)=(\cos 2 t) \mathbf{i}+(\sin 2 t) \mathbf{j}+5 t \mathbf{k}$
$0 \leq t \leq 2 \pi$



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