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JEE Main202621 January 2026Morning ShiftMathematicsDefinite IntegrationActual

The value of _ - / 6 ^ / 6 ( +4 x¹¹ 1- (|x|+ / 6) ) d x is equal to:

Options

  1. A8
  2. B6
  3. C2
  4. D4

Correct answer

D. 4

Step-by-step solution

Split: _ - /6 ^ /6 1 - (|x| + /6) dx + _ - /6 ^ /6 4x¹¹ 1 - (|x| + /6) dx . Second integral = 0 (odd function over symmetric interval). First integral: 2 ₀^ /6 1 1 - (x + /6) dx . Let u = x + /6 : = 2 _ /6 ^ /3 1 1 - u du . 1 1- u = ^2 u + u u . = 2 [ u + u]_ /6 ^ /3 = 2 [( 3 +2) - 3 ] = 4 .

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