29.34. Calculate the length of the arc of the parabola $2 y=x^{2}$ from the point $(0,0)$ to the point $\left(x_{0}, \frac{x_{0}^{2}}{2}\right)$.
29.34. The length of the considered arc of the parabola is equal to

$$
\int_{0}^{x_{0}} \sqrt{1+y'^2} d x=\int_{0}^{x_{0}} \sqrt{1+x^{2}} d x=\frac{x_{0} \sqrt{1+x_{0}^{2}}}{2}+\frac{1}{2} \ln \left(x_{0}+\sqrt{1+x_{0}^{2}}\right)
$$

(see problem 29.7).