9.4.5 Curvilinear integrals

3 Problem: Calculate the line integral: \[ \int_{L} \sqrt{\frac{a^{2}}{b^{2}} y^{2}+\frac{b^{2}}{a^{2}} x^{2}} d L \] where \( L:\left\{\begin{array}{l}x=a \cos t \\ y=b \sin t\end{array}, \quad 0 \leq t \leq \frac{\pi}{2}\right. \).