9.4.17 Curvilinear integrals

Problem: Calculate the first kind of line integrals along curves given parametrically: a) \( \int_{L}(x+z) d l \), where \( L:\left\{\begin{array}{c}x=t \\ y=\frac{3 t^{2}}{\sqrt{2}}, \quad 0 \leq t \leq 1, \\ z=t^{2}\end{array}\right. \) b) \( \int_{L} \frac{d l}{x^{2}+y^{2}+z^{2}} \), where \( \quad L:\left\{\begin{array}{c}x=a \cos t \\ y=a \sin t \text { is the } 1 \text { st turn. } \\ z=b t\end{array}\right. \)