9.4.23 Curvilinear integrals

令 Problem: Find the center of gravity of a spatial curve with linear density \( M(x, y, z) \), given parametrically: \[ \ell:\left\{\begin{array}{l} x=a \cos t \\ y=a \sin t \\ z=b t \end{array} \quad\left(0 \leq t \leq \frac{\pi}{2}\right), \quad M(x, y, z)=c \cdot x y .\right. \]