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JEE Main2013MathematicsDefinite IntegrationActual

Statement - I : The value of the integral ∫ π / 6 π / 3 d x 1 + tan x is equal to π 6 . Statement - II : ∫ a b f x d x = ∫ a b f a + b - x d x .

Options

  1. AStatement - I is true; Statement - II is false.
  2. BStatement - I is false; Statement - II is true.
  3. CStatement - I true; Statement - II is true; Statement - II is a correct explanation for Statement - I .
  4. DStatement - I is true; Statement - II is true; Statement - II is not a correct explanation for Statement - I .

Correct answer

B. Statement - I is false; Statement - II is true.

Step-by-step solution

Statement II is a standard property of definite integrals. For statement I : I = ∫ π / 6 π / 3 d x 1 + tan   x = ∫ π / 6 π / 3 d x 1 + cot   x I = ∫ π / 6 π / 3 tan   x 1 + tan   x d x = ∫ π / 6 π / 3 sin x cos x + sin x d x = ∫ π / 6 π / 3 cos x cos x + sin x d x 2 I = ∫ π / 6 π / 3 d x 2 I = π 3 - π 6 I = π 1 2 Hence, statement I is false.

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