With \(\mathbf{v}\) as in Exercise 59, calculate the flow rate across the part of the elliptic cylinder \(\frac{x^{2}}{4}+y^{2}=1\), where \(x \geq 0, y \geq 0\), and \(0 \leq z \leq 4\).

Data From Exercise 59

Find the flow rate of a fluid with velocity field \(\mathbf{v}=\langle 2 x, y, x yangle \mathrm{m} / \mathrm{s}\) across the part of the cylinder \(x^{2}+y^{2}=\) 9 where \(x \geq 0, y \geq 0\), and \(0 \leq z \leq 4\) (distance in meters).