∫41{|x−1|+|x−2|+|x−3|}dx
∫41{|x−1|+|x−2|+|x−3|}dx=∫21(|x−1|+|x−2|+|x−3|)dx+∫32{|x−1|+|x−2|+|x−3|}dx+∫43{|x−1|+|x−2|+|x−3|}dx=∫21{x−1−(x−2)−(x−3)}dx+∫32(x−1+x−2−(x−3)dx+∫43(x−1+x−2+x−3)dx=∫21(−x+4)dx+∫32x dx+∫43(3x−6)dx=[−x22+4x]21+[x22]32+[3x22−6x]43=(−222+8)−(−12+4)+12(32−22)+(32×42−6×4)−(32×32−6×3)=6−72+52+(24−24)−(−92)=12−7+52+0+92=192