Question

\text { Evaluate } \int_{C} \mathbf{v} \cdot d \mathbf{r} \text { in the case that } \mathbf{v}=\left(-x y+5 y+3,-y^{2}-5 x-2 z, \quad 2 x z+1\right) and C is the helix

parametrised by \mathbf{r}(t)=(\cos (t), \sin (t), t), \text { for } t \in[0, \pi] Enter only the final answer in exact form (no decimal approximations). Youmay need to use the oo palette to access symbols. \int_{C} \mathbf{v} \cdot d \mathbf{r}=

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7