Problem

PART 1: Fill in the blanks.

• Work need not be shown, only answers will be graded.

• 4 points for each blank and 100 points total.

• Each answer need to be clearly labeled on the answer sheet.

• Use of any device with computer algebra system during the exam will result in zero points.

18. Let $\vec{F}(x,y,z)=(\sin y,x\cos y+\cos z,-y\sin z),C:\vec{r}(t)=(\sin t,\cos t,2t),0\le t\le \pi$.

$\displaystyle\int_C \vec{F}\cdot d\vec{r}=\underline{\quad(23)\quad}$.