91Ó°ÊÓ

In Exercises \(63-68,\) use a CAS to perform the following steps for finding the work done by force F over the given path: $$\begin{array}{l}{\mathbf{F}=\frac{3}{1+x^{2}} \mathbf{i}+\frac{2}{1+y^{2}} \mathbf{j} ; \quad \mathbf{r}(t)=(\cos t) \mathbf{i}+(\sin t) \mathbf{j}} \\\ {0 \leq t \leq \pi}\end{array}$$

In Exercises \(63-68,\) use a CAS to perform the following steps for finding the work done by force F over the given path: $$\begin{array}{l}{\mathbf{F}=(y+y z \cos x y z) \mathbf{i}+\left(x^{2}+x z \cos x y z\right) \mathbf{j}+} \\ {(z+x y \cos x y z) \mathbf{k} ; \quad \mathbf{r}(t)=(2 \cos t) \mathbf{i}+(3 \sin t) \mathbf{j}+\mathbf{k}} \\ {0 \leq t \leq 2 \pi}\end{array}$$

In Exercises \(63-68,\) use a CAS to perform the following steps for finding the work done by force F over the given path: $$\begin{array}{l}{\mathbf{F}=2 x y \mathbf{i}-y^{2} \mathbf{j}+z e^{x} \mathbf{k} ; \quad \mathbf{r}(t)=-t \mathbf{i}+\sqrt{t} \mathbf{j}+3 t \mathbf{k}} \\ {1 \leq t \leq 4}\end{array}$$

In Exercises \(63-68,\) use a CAS to perform the following steps for finding the work done by force F over the given path: $$\begin{array}{l}{\mathbf{F}=(2 y+\sin x) \mathbf{i}+\left(z^{2}+(1 / 3) \cos y\right) \mathbf{j}+x^{4} \mathbf{k}} \\ {\mathbf{r}(t)=(\sin t) \mathbf{i}+(\cos t) \mathbf{j}+(\sin 2 t) \mathbf{k}, \quad-\pi / 2 \leq t \leq \pi / 2}\end{array}$$

In Exercises \(63-68,\) use a CAS to perform the following steps for finding the work done by force F over the given path: $$\begin{array}{l}{\mathbf{F}=\left(x^{2} y\right) \mathbf{i}+\frac{1}{3} x^{3} \mathbf{j}+x y \mathbf{k} ; \quad \mathbf{r}(t)=(\cos t) \mathbf{i}+(\sin t) \mathbf{j}+} \\ {\left(2 \sin ^{2} t-1\right) \mathbf{k}, \quad 0 \leq t \leq 2 \pi}\end{array}$$