Evaluate the definite integral:
Given:
First solve for I1:
As we can see that (x-1)≥0 when 1≤x≤4
Now solve for I2:
As we can see that (x-2)≤0 when 1≤x≤2 and (x-2)≥0 when 2≤x≤4
Now solve for I3:
As we can see that (x-3)≤0 when 1≤x≤3 and (x-3)≥0 when 3≤x≤4