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NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

The value of Ι = l i m n → ∞ ∑ r = n 2 n n r 2 is equal to

Options

  1. A1 3
  2. B1 2
  3. Cπ 2
  4. Dπ 3

Correct answer

B. 1 2

Step-by-step solution

Ι = l i m n → ∞ ∑ r = n 2 n 1 r 2 n 2 ⋅ 1 n = ∫ 1 2 1 x 2 d x = - 1 x 1 2 = - 1 2 - - 1 = 1 2

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