Calculus problem #2069

Calculus Level 4

Consider the vector function given by F(x,y,z)=z i+y jx kF(x,y,z)=z\ \boldsymbol{i}+y\ \boldsymbol{j}-x\ \boldsymbol{k}. Let CC be the curve given by r(t)=t i+sint j+cost k\boldsymbol{r}(t)=t\ \boldsymbol{i} + \sin t\ \boldsymbol{j} + \cos t\ \boldsymbol{k}, where 0tπ0 \leq t \leq \pi. What is the value of

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

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