Statement - I : The value of the integral `int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx))` is equal to `pi/6` . Statement - II : `int_a^bf(x)dx=int_a^bf(a+b-x)dxdot` (1) Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I (2) Statement -I is True; Statement -II is False. (3) Statement -I is False; Statement -II is True (4) Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

Explanation

`i = int_(pi/6)^(pi/3) dx/(1 + sqrt tan x) `

`= int_(pi/6)^(pi/3) dx/(1 + sqrt(tan(pi/3 + pi/6 - x))`

`= int_(pi/6)^(pi/3) dx/(1 + sqrt cot x) `

`= int_(pi/6)^(pi/3) (sqrt tan x)/(sqrt tan x + 1) dx`

equation `1+ 2`

`2i = int_(pi/6)^(pi/3) (1 + sqrt tan x)/(1 + sqrt tan x) dx`

`2i = x`

`2i = pi/3 - pi/6`

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