Lời giải

\( S = \int_{0}^{\frac{\sqrt{2}}{2}} \left| \frac{x}{\sqrt{1 - x^4}} \right| dx = \int_{0}^{\frac{\sqrt{2}}{2}} \frac{x}{\sqrt{1 - x^4}} dx \)

Đặt  \( x^2 = \sin t, \quad -\frac{\pi}{2} \leq t \leq \frac{\pi}{2} \)

\( \Rightarrow 2x dx = \cos t \, dt \quad \Rightarrow x dx = \frac{1}{2} \cos t \, dt \)

\(  \begin{cases}
x = 0 & \Rightarrow t = 0\\
x = \frac{\sqrt{2}}{2} & \Rightarrow t = \frac{\pi}{6}
\end{cases}\)

\( S = \frac{1}{2}\int_{0}^{\frac{\pi}{6}} \frac{\cos t}{\sqrt{1 - \sin^2 t}} dt = \frac{1}{2} \int_{0}^{\frac{\pi}{6}}  \, dt = \frac{\pi}{12} \) (đvdt)