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AP EAMCET2005MathematicsDefinite Integration

₀^ 1+ ^2 d is equal to

Options

  1. A^2 2
  2. B^2 3
  3. C^2
  4. D^2 4

Correct answer

D. ^2 4

Step-by-step solution

= ₀^ ( - ) ( - ) 1+ ^2( - ) d On adding Eqs. (i) and (ii), we get 2 I= ₀^ 1+ ^2 d Let =t - d =d t aligned 2 I & =- ₁⁻¹ 1 1+t^2 d t & =2 ₀^1 1 1+t^2 d t & =2 [ ⁻¹ t ]₀^1=2 4 aligned I= ^2 4

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