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NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

If A n = ∫ 0 n π sin ⁡ x d x , ∀ n ∈ N , then ∑ r = 1 10 A r is equal to

Options

  1. A100
  2. B110
  3. C55
  4. D105

Correct answer

B. 110

Step-by-step solution

As the period of y = sin ⁡ x is π , hence A n = n ∫ 0 π sin ⁡ x d x = n ∫ 0 π sin ⁡ x d x = n - cos ⁡ x 0 π = 2 n ∴ ∑ r = 1 10 A r = ∑ r = 1 10 2 r = 2 1 + 2 + . . . . + 10 = 2 × 10 × 11 2 = 110

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