# How do I evaluate #int_0^5|x-5|dx# by interpreting it in terms of areas?

##### 1 Answer

Both equations

graph{|x-5| [-5.37, 14.63, -1, 9]}

As you can see, before the abscissa 5 (i.e.,

If you want to integrate the function over the interval

If you say "by interpreting it in terms of areas", I assume that you don't want the explicit calculation of the integral. If so, it should be clear from the figure that the area you're looking for is the one of the triangle with vertices

It is a right triangle with both catheti long 5, and so you can easily find the area, which is

If my supposition was wrong, and you actually need the integral to be done, here are the steps:

First of all, remark that in your range of integration (i.e. the interval