Statement-1: The value of the integral ∫ π /6 ^(π /3) dx/(1 + √(tan x)) is equal to π /6 Statement-2: ∫ a ^(b) f(x) dx = ∫ a ^(b) f(a + b - x) dx.

(D) Statement-1 is false; Statement-2 is true.

(A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

(C) Statement- 1 is true; Statement-2 is False.

Integral Calculus: JEE Main 2013 Mathematics question

JEE Main 2013 · Session, Shift 1 · Q3349

JEE Main 2013Session, Shift 1MathematicsMediumIntegral Calculus369× since 2002

Statement-1 : The value of the integral

\int\limits_{\pi /6}^{\pi /3} {{{dx} \over {1 + \sqrt {\tan \,x} }}}

is equal to

\pi /6

Statement-2 :

\int\limits_a^b {f\left( x \right)} dx = \int\limits_a^b {f\left( {a + b - x} \right)} dx.

JEE Main 2013 · Session, Shift 1 · Q3349

JEE Main 2013Session, Shift 1MathematicsMediumIntegral Calculus369× since 2002

Statement-1 : The value of the integral

\int\limits_{\pi /6}^{\pi /3} {{{dx} \over {1 + \sqrt {\tan \,x} }}}

is equal to

\pi /6

Statement-2 :

\int\limits_a^b {f\left( x \right)} dx = \int\limits_a^b {f\left( {a + b - x} \right)} dx.