The value of `int_0^((3pi)/2)(|tan^(-1)tanx|-|sin^(-1)sinx|)/(|tan^(-1)tanx|+|sin^(-1)sinx|)dx` is equal to

Answer

0

Explanation

`:'` integrand is discontinous at `(pi)/2 , int_(0)^(pi//2)0. dx+int_(pi//2)^(3pi//2) 0 . dx=0`
`:' 0 lt x (pi)/2,|tan^(-1)tanx|`
`=|sin^(-1)sinx|` and `(pi)/2lt xlt (3pi)/2|tan^(-1)tanx|=|sin^(-1)sinx|`