What is the area of the region in the first quadrant bounded by $y^{2} = 9x$, the $x$-axis and the lines $x = 1$ and $x = 4$?

Explanation

1. 01

   In the first quadrant $y = 3\sqrt{x}$: $\int_1^{4} 3\sqrt{x}\,dx = 2\left[x^{3/2}\right]_1^{4}$.

2. 02

   $2(8 - 1) = 14$ square units.