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NTA Abhyas JEE Main2020MathematicsIndefinite IntegrationPractice

The value of the integral ∫ c o s e c 2 x - 2019 c o s 2019 x d x is equal to (where C is the constant of integration)

Options

  1. Acot ⁡ x cos ⁡ x 2019 + C
  2. B- cot ⁡ x cos ⁡ x 2019 + C
  3. Ccot ⁡ x cos ⁡ x 2019 + C
  4. D- cot ⁡ x cos ⁡ x 2019 + C

Correct answer

B. - cot ⁡ x cos ⁡ x 2019 + C

Step-by-step solution

∫ c o s e c 2 x cos ⁡ x - 2019 d x - ∫ 2019 cos ⁡ x 2019 d x = - cot ⁡ x cos ⁡ x - 2019 + ∫ cot ⁡ x 2019 cos ⁡ x - 2020 sin ⁡ x d x - ∫ 2019 cos ⁡ x - 2019 d x = - cot ⁡ x cos ⁡ x 2019 + C

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