Question

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

Answer 1

The region under the graph of `f(x)=|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 `\frac{1}{2}\cdot 5\cdot 5=\frac{25}{2}`. Altogether the total area is 25, and this is the value of the definite integral `\int_{0}^{10}f(x)\ dx`.

graph{|x-5| [-5.33, 14.67, -2.8, 7.2]}