`int_(2)^(8)|x-5|dx`

Explanation

माना `I=int_(2)^(8)|x-5|dx`
`rArr" "I=int_(2)^(5){-(x-5)}dx+int_(5)^(8)(x-5)dx`
`=int_(2)^(5)(5-x)dx+int_(5)^(8)(x-5)dx`
`=[5x-(x^(2))/(2)]_(2)^(5)+[(x^(2))/(2)-5x]_(5)^(8)`
`=(25-(25)/(2))-(10-(4)/(2))+((64)/(2)-40)-((25)/(2)-25)`
`=(25)/(2)-8-8+(25)/(2)=25-16=9`