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JEE Main20249 Apr 2024Evening ShiftMathematicsInverse Trigonometric FunctionsActual

The integral _ 1 / 4 ^ 3 / 4 (2 ⁻¹ 1-x 1+x ) d x is equal to

Options

  1. A1 / 2
  2. B-1 / 2
  3. C-1 / 4
  4. D1 / 4

Correct answer

C. -1 / 4

Step-by-step solution

aligned & I= _ 1 / 4 ^ 3 / 4 (2 ⁻¹ ( 1-x 1+x ) d x ) & _ 1 / 4 ^ 3 / 4 (2 ( ⁻¹ 1+x 1+x ) ) d x & . _ 1 / 4 ^ 3 / 4 1- ^2 ( ⁻¹ 1+x 1-x ) 1+ ^2 ( ⁻¹ 1+x 1-x . ) d x aligned aligned & = _ 1 / 4 ^ 3 / 4 1- ( 1+x 1-x ) 1+ ( 1+x 1-x ) d x= _ 1 / 4 ^ 3 / 4 -2 x 2 d x & = _ 1 / 4 ^ 3 / 4 (-x) d x=- ( x^2 2 )_ 1 / 4 ^ 3 / 4 & =- 1 2 [ 9 16 - 1 16 ] & =- 1 4 aligned

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