Using horizontal strips, which integral gives the area of the triangle bounded by the lines $x = 2y$, $x = 8 - 2y$ and the $x$-axis?

Explanation

1. 01

   The lines meet where $2y = 8 - 2y$, at $y = 2$. A strip at height $y$ runs from $x = 2y$ to $x = 8 - 2y$.

2. 02

   Its length is $(8 - 2y) - 2y = 8 - 4y$, so the area is $\int_0^{2} (8 - 4y)\,dy = 8$ square units.