Chapter 16.5, Problem 24E

To determine

To calculate : The flow rate (in cubic meters per second) of a fluid with velocity field $v=\langle x,y,x^{2}y\rangle$(in m/s) through the portion of the ellipse ${\left(\frac{x}{2}\right)}^2+{\left(\frac{y}{3}\right)}^2=1$ in the xy-plane, where $x,y\ge 0$ oriented with the normal in the positive z-direction.