`int_(0)^(1)|5x-3|dx` का मान ज्ञात कीजिए।

Explanation

`|5x-3|={{:(5x-3",",xle3//5),(-(5x-3)",",xlt3//5):}`
`therefore" "int_(0)^(1)|5x-3|dx=int_(0)^(3//5)|5x-3|dx+int_(3//5)^(1)|5x-3|dx`
`=int_(0)^(3//5)-(5x-3)dx+int_(3//5)^(1)(5x-3)dx`
`=-[(5x^(2))/(2)-3x]_(0)^(3//5)+[(5x^(2))/(2)-3x]_(3//5)^(1)`
`=-[(5)/(2)xx(9)/(25)-3xx(3)/(5)-0]+[((5)/(2)-3)-((5)/(2)xx(9)/(25)-3xx(3)/(5))]`
`=-(9)/(10)+(9)/(5)-(1)/(2)-(9)/(10)+(9)/(5)`
`=-(18)/(10)+(18)/(5)-(1)/(2)=(-18+36-5)/(10)`
`=(13)/(10)`