The value of `[int_(-pi)^(pi) sqrt((|sinx|)/(1+tan^(2)x))dx]` is (where [.] is greates integer).

Answer

2

Explanation

`I=int_(-pi)^(pi) sqrt((|sinx|)/(1+tan^(2)x))dx`
`I=2int_(-(pi)/2)^((pi)/2)sqrt((sinx)/(1+cot^(2)x))dx`
`4 int_(0)^((pi)/2) sqrt(cosx) sin x dx`
`=8/3`
`[I]=2`