Answer
$-0.1363$
Work Step by Step
Here, $dr=(-\sin t i+\cos t j+5 \cos 5tk) dt$ and $F(r(t))=|\sin t| \sin [\sin 5 t] i +|\sin 5t| \sin [\cos t] j+\cos t \sin [\sin t] k$
$\int_{C} \overrightarrow{F} \cdot \overrightarrow{dr}=\int_0^{\pi} (|\sin t| \sin [\sin 5 t] i +|\sin 5t| \sin [\cos t] j+\cos t \sin [\sin t] k) \cdot (-\sin t i+\cos t j+5 \cos 5tk) dt) d t$
By using the calculator, we have $\int_{C} \overrightarrow{F} \cdot \overrightarrow{dr}=-0.1363$
