GATE Electronics and Communications (EC) 2022 Solved Paper

In an electrostatic field, the electric displacement density vector D is given by
$\overrightarrow{\mathit{D}}\left(\mathit{x},\mathit{y},\mathit{z}\right)=\left({\mathit{x}}^3\hat{\mathit{i}}+{\mathit{y}}^3\hat{\mathit{j}}+\mathit{x}{\mathit{y}}^2\hat{\mathit{k}}\right)$ C/m²,
Where,  $\hat{\mathit{i}},\hat{\mathit{j}},\hat{\mathit{k}}$   are the unit vectors along the x-axis, y-axis, and z-axis, respectively. Consider a cubical region 𝑅 centered at the origin with each side of length 1 m, and vertices at (± 0.5 m, ± 0.5 m, ± 0.5 m). The electric charge enclosed within 𝑅 is _________ C (rounded off to two decimal places).