Statement - I: The value of the integral _π/6^π/3 dx/1 + √(x) is equal to π/6 .Statement - II: _a^b f(x) dx = _a^b f(a + b - x) dx . - Mathematics MCQ JEE Main 2026 | ExamTest.live

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Statement - I: The value of the integral \int_{π /6}^{π /3} \frac{d x}{1 + t a n x} is equal to π /6 .Statement - II: \int_{a}^{b} f (x) d x = \int_{a}^{b} f (a + b - x) d x .

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 $Statement - I is True; Statement - II is True; Statement - II is a correct explanation for Statement - I$

Solution & Step-by-step Explanation

1. Let I = \int_{π /6}^{π /3} \frac{c o s x}{s i n x + c o s x} d x .2. Using Statement II: x \to \frac{π}{6} + \frac{π}{3} - x = \frac{π}{2} - x . I = \int_{π /6}^{π /3} \frac{s i n x}{c o s x + s i n x} d x .3. 2 I = \int_{π /6}^{π /3} 1 d x = \frac{π}{3} - \frac{π}{6} = \frac{π}{6} .4. I = π /12 .Statement I says I = π /6, which is False. Statement II is a standard property of definite integrals, which is True.

Try it yourself before checking the explanation above.

Statement - I: The value of the integral \int_{π /6}^{π /3} \frac{d x}{1 + t a n x} is equal to π /6 .Statement - II: \int_{a}^{b} f (x) d x = \int_{a}^{b} f (a + b - x) d x .

Statement - I is True; Statement - II is True; Statement - II is not a correct explanation for Statement - I

Statement - I is True; Statement - II is False.

Statement - I is False; Statement - II is True

Statement - I is True; Statement - II is True; Statement - II is a correct explanation for Statement - I

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