Calculate areas of $0 \leq x \leq \sqrt{y}, 0 \leq y \leq \sqrt{x}, x+y \leq 3 / 4$ I have to calculate the areas of this set.
Could someone explain me how do I have to interprete the following:
\begin{equation}
\left\{(x, y) \in \mathbb{R}^{2}: 0 \leq x \leq \sqrt{y}, 0 \leq y \leq \sqrt{x}, x+y \leq 3 / 4\right\}
\end{equation}
Thank you in advance.


The purple area is the part under $y=x^2$ plus the small triangle,
$$\int_0^{1/2} x^2 dx + \frac12 \left(\frac34 - \frac12\right)^2 = \frac7{96} $$
Then, the blue area is the difference between the large triangle and twice of purple.
$$\frac12 \left(\frac34\right)^2 - 2\cdot\frac7{96} = \frac{13}{96}$$
