Question

Statement - I : The value of the integral ${\int }_{\pi /6}^{\pi /3}\frac{dx}{1+\sqrt{\tan x}}$ is equal to $\frac{\pi }{6}$
Statement -II : ${\int }_a^{b}f\left(x\right)dx$ $={\int }_a^{b}f(a+b-x)dx$

• A. Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I
• B. Statement -I is True; Statement -II is False.
• C. Statement -I is False; Statement -II is True
• D. Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

Answer 1

Answer: (C)

Statement -I is False; Statement -II is True

$I={\int }_{\pi /6}^{\pi /3}\frac{dx}{1+\sqrt{\tan x}}$
$I={\int }_{\pi /6}^{\pi /3}\frac{\sqrt{\tan x}}{1+\sqrt{\tan x}}dx$
$2I=\frac{\pi }{6}$
$I=\frac{\pi }{12}$
Therefore, I is false and II is true.
Hence, option 'C' is correct.