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MHT CET202613 April 2026Morning ShiftMathematicsDefinite IntegrationActual

If ₀^a dx 1 + 4x^2 = 8 , then a =

Options

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

Correct answer

B. 1 2

Step-by-step solution

Given ₀^a dx 1 + 4x^2 = 8 Let 2x = t 2dx = dt When x = 0 , t = 0 and when x = a , t = 2a The integral becomes 1 2 ₀^ 2a dt 1 + t^2 = 8 1 2 [ ⁻¹ t]₀^ 2a = 8 1 2 ⁻¹(2a) = 8 ⁻¹(2a) = 4 2a = ( 4 ) = 1 a = 1 2 Answer: 1 2

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