Calculus problem #2069

Calculus Level 4

Consider the vector function given by $F(x,y,z)=z\ \boldsymbol{i}+y\ \boldsymbol{j}-x\ \boldsymbol{k}$ . Let $C$ be the curve given by $\boldsymbol{r}(t)=t\ \boldsymbol{i} + \sin t\ \boldsymbol{j} + \cos t\ \boldsymbol{k}$ , where $0 \leq t \leq \pi$ . What is the value of

$N = \int_C \boldsymbol{F} \cdot d \boldsymbol{r} ?$