9.4.20 Curvilinear integrals

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