What is the area of the region in the first quadrant bounded by $x^{2} = 4y$, the $y$-axis and the lines $y = 1$ and $y = 4$?

Explanation

1. 01

   The region lies against the $y$-axis, so use horizontal strips: $x = 2\sqrt{y}$, $\int_1^{4} 2\sqrt{y}\,dy$.

2. 02

   $\frac{4}{3}\left[y^{3/2}\right]_1^{4} = \frac{4}{3}(8 - 1) = \frac{28}{3}$ square units.