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NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

If f k - x + f x = sin ⁡ x, then the value of integral Ι = ∫ 0 k f x d x is equal to

Options

  1. Acos ⁡ k
  2. B2 c o s 2 k 2
  3. Cs i n 2 k 2
  4. Dsin ⁡ k

Correct answer

C. s i n 2 k 2

Step-by-step solution

Applying property of a + b – x and adding, we get, 2 Ι = ∫ 0 k f x + f k - x d x = ∫ 0 k sin ⁡ x d x = 1 - cos ⁡ k

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