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The value of int0^((3pi)/2)(|tan^(-1)(ta...

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

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Verified by Experts

The correct Answer is:
0
`:'` 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|`
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