To determine the mass of a region where the mass density function $f(x,y) = 1$, we need to know the specific boundaries of the region. However, let's consider a few possible examples of regions to illustrate the process:

Example 1: Rectangular Region

Suppose the region $R$ is a rectangle defined by $a \leq x \leq b$ and $c \leq y \leq d$.

$M = \iint_R 1 \, dA$

The integral becomes:

$M = \int_{a}^{b} \int_{c}^{d} 1 \, dy \, dx$

Evaluating this, we get:

$M = \int_{a}^{b} \left[ y \right]_{c}^{d} \, dx = \int_{a}^{b} (d - c) \, dx$

[ M = (d -