The line $x = c$ divides the region bounded by $y = 2x$, the $x$-axis and the line $x = 4$ into two parts of equal area. What is $c$?

Explanation

1. 01

   The whole region has area $\int_0^{4} 2x\,dx = 16$, so each part has 8.

2. 02

   $\int_0^{c} 2x\,dx = c^{2} = 8$, so $c = 2\sqrt{2}$.