Using integration, what is the area of the triangle with vertices $(1, 0)$, $(5, 0)$ and $(3, 4)$?

Explanation

1. 01

   The sides from the top vertex are $y = 2(x - 1)$ for $1 \le x \le 3$ and $y = 2(5 - x)$ for $3 \le x \le 5$.

2. 02

   $\int_1^{3} 2(x - 1)\,dx + \int_3^{5} 2(5 - x)\,dx = 4 + 4 = 8$ square units.