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JEE Main202124 Feb 2021Morning ShiftMathematicsIndefinite IntegrationActual

If ∫ cos x - sin x 8 - sin 2 x d x = a sin - 1 sin x + cos x b + c , where c is a constant of integration, then the ordered pair a , b is equal to:

Options

  1. A1 , - 3
  2. B3 , 1
  3. C- 1 , 3
  4. D1 , 3

Correct answer

D. 1 , 3

Step-by-step solution

∫ cos x - sin x 8 - sin 2 x d x = ∫ cos x - sin x 9 - sin x + cos x 2 d x Let sin x + cos x = t ∫ d t 9 - t 2 = sin - 1 t 3 + c = sin - 1 sin x + cos x 3 + c So a = 1 ,   b = 3

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