# 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

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

×