Statement - 1 : The value of the integral
`int_(pi/6)^(pi/3) dx/(1 + sqrttanx)` is equal to `pi/6`
Statement-2 : `int_a^b f(x) = int_a^b f(a + b - x) dx`

Options

A. Statement I is true, statement II is true, statement II is a correct explanation for statement I
B. Statement I is true, statement II is true, statement II is a not a correct explanation for statement I
C. Statement I is true, statement II is false
D. Statement I is false, statement II is true

Answer

D

Explanation

`I=int_(pi//6)^(pi//3) (dx)/(1+sqrt(tanx))`………..i
`I=int_(pi//6)^(pi//3) (dx)/(1+sqrt(cotx))=int_(pi//6)^(pi//3)(sqrt(tanx)dx)/(sqrt(tanx)+1)`………..ii
Adding i and ii
`implies2I=int_(pi//6)^(pi//3) 1 dximplies2I=(pi)/3-(pi)/6`
`implies2I=(pi)/6impliesI=(pi)/12`