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JEE Main2015MathematicsDefinite IntegrationActual

The integral ∫ 2 4 log x 2 log x 2 + log 6 - x 2 d x is equal to

Options

  1. A6
  2. B2
  3. C4
  4. D1

Correct answer

D. 1

Step-by-step solution

I = ∫ 2 4 log x 2 log x 2 + log 6 - x 2 d x I = ∫ 2 4 log 6 - x 2 log 6 - x 2 + log x 2 d x ∵ ∫ a b f x d x = ∫ a b f a + b - x d x 2 I = ∫ 2 4 log x 2 + log 6 - x 2 log 6 - x 2 + log x 2 d x 2 I = ∫ 2 4 1 dx 2 I = x 2 4 ∴     I = 1

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