Answer
$\mathop \smallint \limits_{}^{} \mathop \smallint \limits_{\cal R}^{} 4{\rm{d}}A = 36$
Work Step by Step
Write
$\mathop \smallint \limits_{}^{} \mathop \smallint \limits_{\cal R}^{} 4{\rm{d}}A = 4\mathop \smallint \limits_{}^{} \mathop \smallint \limits_{\cal R}^{} {\rm{d}}A = 4\cdot area\left( {\cal R} \right)$
Since ${\cal R} = \left[ {2,5} \right] \times \left[ {4,7} \right]$ is a square, the area of ${\cal R}$ is
$area\left( {\cal R} \right) = \left( {5 - 2} \right)\cdot\left( {7 - 4} \right) = 9$
So, $\mathop \smallint \limits_{}^{} \mathop \smallint \limits_{\cal R}^{} 4{\rm{d}}A = 4\cdot9 = 36$.
