`int_0^10|x - 5|dx` Evaluate the integral by interpreting it in terms of areas.
To interpret this in terms of area, graph the integrand. The integrand is the function f(x) = |x - 5|.
Then, shade the region bounded by f(x) = |x-5| and the x-axis in the interval [0,10]. (Refer to the attached figure.)
Notice that the bounded region forms two right triangles. So to evaluate the integral, compute the area of each triangle and take the sum.
`int_0^10 |x-5| dx`
`=1/2*5*5 + 1/2*5*5`
Thus, `int_0^10 |x-5| dx = 25` .