Pregunta: Evaluate F. dr, where F(x, y, z) = sin x i + cos y j + xz k and r(t) = { i – tj + tk, 0

The given function is $\mathbf{F}(\mathrm{x},\mathrm{y},\mathrm{z})=\sin \mathrm{x}\mathbf{i}+\cos \mathrm{y}\mathbf{j}+\mathrm{x}\mathrm{z}\mathbf{k}$ and $\mathbf{r}\left(\mathrm{t}\right)={\mathrm{t}}^3\mathbf{i}-{\mathrm{t}}^2\mathbf{j}+\mathrm{t}\mathbf{k}$ , $0\le \mathrm{t}\le 1$ .

Find the value of the integral ${\int }_{\mathrm{C}}\mathbf{F}\cdot \mathrm{d}\mathbf{r}$ .

The given integral can be written a...