Let $D(x)$ be a known curve function of $x$. Let $y=\alpha$ be an unknown function parallel to $x$ axis. I want to find $y=\alpha$, which intersects $D(x)$ at two locations such that the intersecting area between the two functions equal to $b$, which is a given value (known value). How can I find $y=\alpha$ function that satisfies these requirements?
(I want to find the value of $\alpha$ and two intersecting values $x_1$ and $x_2$ for which the area in between the two functions is a given value).
1 - find the intersection pts as functions of $\alpha$ satisfying $$ D(x_1(\alpha) ) =D(x_2(\alpha)) = \alpha $$ 2 - solve for $\alpha$ using
$$ \int_{x_1(\alpha) } ^{x_2(\alpha) }|\alpha - D(x)|dx =b $$
Whether or not either of these steps can be actually carried out depends on the nature of $D(x)$