$\displaystyle \left| \underline{v} \right|= \left| \frac{d \underline{r}}{dt} \right|=\left| 2i+j-2k \right|=3$Evaluate $\displaystyle \int_C(xy+y+z)~ds$ along the curve $\displaystyle \underline{r}(t)=2ti+tj+(2-2t)k$ where $\displaystyle 0 \leq t \leq 1$.

$\displaystyle \int_0^1 2t^2+t+2-2t ~dt=\int_0^1 2t^2-t+2 ~dt= \left[ \frac{2t^3}{3}-\frac{t^2}{2}+2t \right]_0^1=\frac{2}{3}-\frac{1}{2}+2=\frac{13}{6}$

Is this right?