What is the area of the region bounded by $y^{2} = 4x$ and the line $x = 4$?

Explanation

1. 01

   By symmetry, $2\int_0^{4} 2\sqrt{x}\,dx = 4 \times \frac{2}{3}x^{3/2}\Big|_0^{4}$.

2. 02

   $4 \times \frac{2}{3} \times 8 = \frac{64}{3}$ square units.