Integration domain in \(\mathbb{R}^2\)

This applet shows to handle 2D curvilinear bounded sets.

There is a "hidden" box \(M:=\{(x,y)^\top\in \mathbb{R}^2\,: \, x_l\leqslant x \leqslant x_u,\; y_l\leqslant y \leqslant y_u\}\) with \(x_l=y_l=0\) und \(x_u=y_u=1\)

The functions are evaluated following the scheme \( \underline{y}(x), \overline{y}(x)\) for \( x \in [x_u, x_l]\) and \(\underline{x}(y), \overline{x}(y)\) for \(y \in [y_l,y_u]\)

The orange domain is set inside the JavaScript code of the applet.

One hast to take care at the corners!

\(\underline{y}(x)=\)
\(\overline{y}(x)=\)
\(\underline{x}(y)=\)
\(\overline{x}(y)=\)

Try to figure out the functions \(\underline{y}, \overline{y}\) and \(\underline{x}, \overline{x}\), that the orange and yellow set will coincide.