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MHT CET2019Evening ShiftMathematicsIndefinite IntegrationActual

∫ c o s x - s i n x 8 - s i n 2 x d x = 1 p log ⁡ 3 + s i n x + c o s x 3 - s i n x - c o s x + c , then p =……

Options

  1. A6
  2. B1
  3. C3
  4. D12

Correct answer

A. 6

Step-by-step solution

∫ c o s x - s i n x 8 - s i n x = 1 p log ⁡ 3 + s i n x + c o s x 3 - s i n x - c o s x + C Now, = ∫ c o s x - s i n x 9 - 1 + 2 s i n x c o s x d x = ∫ c o s x - s i n x 9 - s i n 2 x + c o s 2 x + 2 s i n x c o s x d x = ∫ c o s x - s i n x 3 2 - c o s x + s i n x 2 d x Put c o s x + s i n x = t - s i n x + c o s x d x = d t = ∫ d t 3 2 - t 2 = 1 2 3 log ⁡ 3 + t 3 - t + C = 1 6 log ⁡ 3 + s i n x + c o s x 3 - s i n x - c o s x + C ∴ p = 6

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