`int_(1)^(4)f(x)dx,` जहाँ `f(x)=|x-1|+|x-2|+|x-3|` का मान ज्ञात कीजिए ।

Explanation

माना `int_(1)^(4)f(x)dx=int_(1)^(2)f(x)dx+int_(2)^(3)f(x)dx+int_(3)^(4)f(x)dx`
`=int_(1)^(2){(x-1)-(x-2)-(x-3)}dx+int_(2)^(3){(x-1)+(x-2)-(x-3)}dx+int_(3)^(4){(x-1)+(x-2)+(x-3)}dx`
`=int_(1)^(2)(-x+4)dx+int_(2)^(3)xdx+int_(3)^(4)(3x-6)dx`
`=-[(x^(2))/(2)+4x]_(1)^(2)+[(x^(2))/(2)]_(2)^(3)+[(3x^(2))/(2)-6x]_(3)^(4)`
`=((5)/(2)+(5)/(2)+(9)/(2))=(19)/(2)`