1.

`int_(1)^(4)(|x-1|+|x-2|+|x-3|)dx`

Answer» `int_(1)^(4){(|x-1|+|x-2|+|x-3|)}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-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)`
`=((-2^(2))/(2)+8)-((-1)/(2)+4)+(1)/(2)(3^(2)-2^(2))+((3)/(2)xx4^(2)-6xx4)-((3)/(2)xx3^(2)-6xx3)`
`=6-(7)/(2)+(5)/(2)+(24-24)-(-(9)/(2))`
`=(12-7+5)/(2)+0+(9)/(2)=(19)/(2)`


Discussion

No Comment Found