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












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