Calculate the area enclosed by the parabola y2 = x + 3y and the Y-axis.

9/2 4/3 5/2 3/4

9/2

y2 = x + 3y $⇒(y-\frac{3}{2})^2=x+\frac{9}{4}$ ⇒ Shaded Area = $-\int\limits_0^3[(y-\frac{3}{2})-\frac{9}{4}]dy=\frac{9}{2}$