Answer
$0$
Work Step by Step
Here, $dr=(-\sin t i+\cos t j+k) dt$ and $F(r(t)=\cos t i +\sin t j+\cos t \sin t k$
$\int_{C} \overrightarrow{F} \cdot \overrightarrow{dr}=\int_0^{\pi} (\cos t i +\sin t j+\cos t \sin t k) \cdot (-\sin t i+\cos t j+k) d t$
or, $= \int_0^{\pi} \cos t \sin t dt$
or, $=\dfrac{1}{2} \int_0^{\pi} 2 \cos t \sin t dt$
or, $\int_{C} \overrightarrow{F} \cdot \overrightarrow{dr}=\dfrac{1}{2} \int_0^{\pi} \sin 2 t dt=(\dfrac{1}{2})[\dfrac{-\cos 2t}{2}]_0^{\pi}=0$
