Evaluate `int_(0)^(pi//2)|sinx-cosx|dx`.

Answer

`2sqrt(2)-1)`

Explanation

`int_(0)^(pi//2)|sinx-cosx|dx`
`=int_(0)^(pi//4)-(sinx-cosx)dx+int_(pi//4)^(pi//2)(sinx-cosx)dx`
`=|cosx+sinx|_(0)^(pi//4)+|-cosx-sinx|_(pi//4)^(pi//2)`
`=(1/(sqrt(2))+1/(sqrt(2))-1-0)+(-0-1+1/(sqrt(2))+1/(sqrt(2)))`
`=4/(sqrt(2))-2=2sqrt(2)-2`
`2(sqrt(2)-1)`