Answer
$\int_{0}^{4}\int_{-4+y}^{4-y}f(x,y) dxdy$
Work Step by Step
Equation of a line joining with $x$- intercept $=a$ and $y$-intercept $=b$ is
$\frac{x}{a}+\frac{y}{b}=1$
Therefore,
Equation of a line joining with both intercepts $4$ is
$\frac{x}{4}+\frac{y}{4}=1$
which can be written as $x=4-y$
Using polar co-ordinates, we can define the region $R$ as follows:
$R=(r,\theta) | 0\leq y\leq 4, -4+y\leq x \leq 4-y$
Therefore,
${\int\int}_{R}f(x,y)dA=\int_{0}^{4}\int_{-4+y}^{4-y}f(x,y) dxdy$
