Question

Tính S: \(\left\{\left(P_1\right)\div x^2=ay;\left(P_2\right)\div y^2=ax\right\}\)         (a>0)

Giúp em với các anh chị

Answer 1

\(\left(P_1\right)\cap\left(P_2\right):\begin{cases}y=\frac{x^2}{a}\\y^2=ax\end{cases}\Leftrightarrow\begin{cases}y^2=\frac{x^4}{a^2}\\y^2=ax\end{cases}}\)

 

\(\Leftrightarrow\hept{\begin{cases}\frac{x^4}{a^2}=ax\\y=ax\end{cases}\Leftrightarrow\hept{\begin{cases}x^4=a^3x\\y^2=ax\end{cases}\Leftrightarrow}\left[\begin{array}{nghiempt}x=0;y=0\\x=a;y=a\end{array}\right.}\)

\(S=\int\limits^a_0\left(\sqrt{ax}-\frac{x^2}{a}\right)dx=\left(\frac{2\sqrt{a}}{3}x\sqrt{x}-\frac{x^3}{3a}\right)|^a_0=\frac{2a^2}{3}-\frac{a^3}{3a}=\frac{a^2}{3}\)