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AP EAMCET2003MathematicsDefinite Integration

₀^1 (2 ⁻¹ 1+x 1-x ) d x is equal to :

Options

  1. A6
  2. B4
  3. C2

Correct answer

B. 4

Step-by-step solution

Let I= ₀^1 (2 ⁻¹ 1+x 1-x ) d x Put x= d x=- d I= _ / 2 ^0 (2 ⁻¹ 1+ 1- )(- ) d = ₀^ / 2 (2 ⁻¹ ( 2 - 2 ) ) d = ₀^ / 2 ( - ) d = ₀^ / 2 ^2 d = ₀^ / 2 [ 1- 2 2 ] d = 1 2 [ - 2 2 ]₀^ / 2 = 1 2 [ 2 -0 = 4

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