9.4.15 Curvilinear integrals

31 Problem: Calculate the line integral of the \( 1^{\text {st }} \) kind along the space curve: \[ \int_{\Gamma}\left(x^{2}+y^{2}+z^{2}\right) d l \] where \( \Gamma \) is the first turn of the helix: \[ \left\{\begin{array}{c} x=a \cos t \\ y=a \sin t, \quad a>0, b>0 . \\ z=b t \end{array}\right. \]