EXAMPLE 1. Calculate the line integral

$$
\int_{L} \frac{z^{2}}{x^{2}+y^{2}} d l
$$

where $L-$ is the first turn of the helical line

$$
\left\{\begin{array}{l}
x=\cos t \\
y=\sin t, \quad 0 \leq t \leq 2 \pi \\
z=t
\end{array}\right.
$$
Solution.

1. Compute: $x^{\prime}(t)=-\sin t, y^{\prime}(t)=\cos t, z^{\prime}(t)=1, d l=\sqrt{2} d t$ and $f(x, y)=z^{2} /\left(x^{2}+y^{2}\right)=t^{2}$.
2. Substitute these results into formula (1) and compute the definite integral:

$$
\int_{L} \frac{z^{2}}{x^{2}+y^{2}} d l=\int_{0}^{2 \pi} t^{2} \sqrt{2} d t=\frac{8 \sqrt{2} \pi^{3}}{3}
$$

Answer. $\int_{L} \frac{z^{2}}{x^{2}+y^{2}} d l=\frac{8 \sqrt{2} \pi^{3}}{3}$.