# How do you evaluate the integral of absolute value of (x - 5) from 0 to 10 by finding area?

The region under the graph of $f \left(x\right) = | x - 5 |$ from $a = 0$ to $b = 10$ is made up of two triangles. The triangles both have a base of length 5 units and a height of 5 units, so they each have an area of $\setminus \frac{1}{2} \setminus \cdot 5 \setminus \cdot 5 = \setminus \frac{25}{2}$. Altogether the total area is 25, and this is the value of the definite integral $\setminus {\int}_{0}^{10} f \left(x\right) \setminus \mathrm{dx}$.