Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using high school geometry.

Question

interval 0 to 11 |3x-15|dx

Answer 1

From x = 0 to 5, |3x-15| goes from 15 to 0, as a straight line.
From x = 5 to 11, |3x-15| goes from 0 to 18, as a straight line.

Compute the areas of the two triangular regions separately, and add them.
(1/2)*5*15 + (1/2)*6*18 = ______