y²=x এবং x²=y বক্ররেখা দ্বারা আবদ্ধ ক্ষেত্রের ক্ষেত্রফল কত বর্গ একক?

$\begin{array}{l}y^{2}=x \dots(i) \\ x^{2}=y \dots(ii)\end{array}$ $\begin{array}{l}(ii)^{2} \Rightarrow y^{2}=x^{4} \\ \Rightarrow x=x^{4} \\ \Rightarrow x^{4}=x \\ \Rightarrow x^{4}-x=0 \\ \Rightarrow x\left(x^{3}-1\right)=0 \\ \Rightarrow x=0,1\end{array}$ $\begin{aligned} A & =\int_{0}^{1}\left(y_{1}-y_{2}\right) d x \\ \Rightarrow A & =\int_{0}^{1}\left(\sqrt{x}-x^{2}\right) d x \\ \Rightarrow A & =\left[\frac{2}{3} x^{\frac{3}{2}}-\frac{1}{3} x^{3}\right]_{0}^{1} \\ \Rightarrow A & =\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\end{aligned}$

$\begin{array}{l}y^{2}=x \\ \Rightarrow y_{1}=\sqrt{x} \\ y_{2}=x^{2}\end{array}$