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JEE Main2014MathematicsIndefinite IntegrationActual

∫ sin 8 x - cos 8 x 1 - 2 sin 2 x cos 2 x d x is equal to

Options

  1. A- 1 2 sin 2 x + c
  2. B- sin 2 x + c
  3. C- 1 2 sin x + c
  4. D1 2 sin 2 x + c

Correct answer

A. - 1 2 sin 2 x + c

Step-by-step solution

sin 8 x - cos 8 x = sin 2 x - cos 2 x sin 2 x + cos 2 x sin 4 x + cos 4 x and sin 4 x + cos 4 x = sin 2 x + cos 2 x 2 - 2 sin 2 x cos 2 x = 1 - 2 sin 2 x cos 2 x ∴ I = ∫ sin 8 x - cos 8 x 1 - 2 sin 2 x cos 2 x d x = ∫ sin 2 x - cos 2 x sin 4 x + cos 4 x sin 4 x + cos 4 x d x = - ∫ cos 2 x d x = - 1 2 sin 2 x + c , where c is the constant of integration.

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