Evaluate:

  [CBSE 2017]

We need  to find the correct limits for expanding this integration. And for that we need to look at the graph:



(i) For |x - 1|, From x = 1 to x = 4, (x - 1) is positive. So we will take positive value. i.e, (x - 1).

(ii) For |x - 2|, From x = 1 to x = 2, |x - 2| is negative and from x = 2 to x = 4, |x - 2| is positive.
Therefore, the limits are x = 1 to x = 2, y = -(x - 2) and from x = 2 to x = 4, y = (x - 2).

(iii) For |x - 4|, From x = 1 to x = 4, |x - 4| is negative. Therefore, from x = 1 to x = 4, y = -(x - 4) .