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NTA Abhyas JEE Main2020MathematicsIndefinite IntegrationPractice

The integral I = ∫ 2 2 x + x d x = λ . 2 2 x + C (where, C is the constant of integration). Then the value of λ is equal to

Options

  1. A1 ln ⁡ 4
  2. B1 ln ⁡ 2 2
  3. C1 ln ⁡ 2
  4. D1 ln ⁡ 4 2

Correct answer

C. 1 ln ⁡ 2

Step-by-step solution

Given, I = ∫ 2 2 x . 2 x d x Let, 2 2 x = t ⇒ 2 2 x . 2 x . ln ⁡ 2 2 d x = d t ⇒ 2 2 x . 2 x d x = d t ln ⁡ 2 2 Thus, I = ∫ d t ln ⁡ 2 2 = t ln ⁡ 2 2 + C = 2 2 x ln ⁡ 2 2 + C ∴ λ = 1 ln ⁡ 2 2 ⇒ λ = l ln ⁡ 2

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