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NTA Abhyas JEE Main2020MathematicsIndefinite IntegrationPractice

The least value of n   n ∈ N , such that the function f n , x = ∫ n cos ⁡ n x d x satisfies f n , π 2 = - 1 , is (given, f n , 0 = 0 )

Options

  1. A3
  2. B4
  3. C5
  4. D6

Correct answer

A. 3

Step-by-step solution

Given function is f n , x = n ⋅ sin n x n + c As f n , 0 = 0 ⇒ c = 0 ∴ f n , x = sin ⁡ n x If f n , π 2 = - 1 , we have sin ⁡ n π 2 = - 1 ⇒ n = 3 , 7 , 11 , … … ∴ n m i n = 3

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