Can we possibly compute the following integral in terms of known constants? $$\displaystyle \int_{0}^{1}\int_{0}^{1}\frac{dxdy}{1-xy(1-x)(1-y)}$$ Some progress was already done here http://integralsandseries.prophpbb.com/topic279.html but still we have a hypergeometric function. What's your thou...

We assume that a mountain has the shape of the elliptic paraboloid $z=c-ax^2-by^2$, where $a$, $b$ and $c$ are positive constants, $x$ and $y$ are the geographical coordinates (east-west, north-south respectively), and $z$ is the altitude above the sea level (the $x$, $y$, $z$ are all measured in...