\int_{1}^{0}\int_{4}^{0} (xy) \text{d}x \text{d}y = \int_{4}^{0} (xy) \text{d}x \text{d}y = \left[\frac{x^2}{2} \cdot y\right]_{0}^{4} = \left[\frac{0^2}{2} \cdot y\right] - \left[\frac{4^2}{2} \cdot y\right] = \left[0\right] - \left[\frac{16}{2} \cdot y\right] = \left[0\right] - \left[8 \cdot y\right] = \mathbf{-8y} =>\int_{1}^{0}\int_{4}^{0} ((xy) \text{d}x) \text{d}y = \int_{1}^{0}(-8y)\text{d}y ={\left[\frac{-8y^2}{2}\right]_{0}^{1}} = \left[-4y^2\right]_{0}^{1}= 0-(-4) = \mathbf{4}