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AP EAMCET202422 May 2024Morning ShiftMathematicsDefinite IntegrationActual

_ - ^ x x 1+ ^2 x d x=

Options

  1. A3 ^2 4
  2. B2 +1
  3. C^2 4
  4. D^2 2

Correct answer

D. ^2 2

Step-by-step solution

aligned & I= _ - ^ x x 1+ ^2 x d x ....(i) & I=2 ₀^ x x 1+ ^2 x & I=2 ₀^ ( -x) x 1+ ^2 x d x.....(ii) aligned Adding (i) and (ii) 2 I=2 ₀^ x 1+ ^2 x d x Let x=t d t=- x d xI= _ -1 ^1 -1 1+t^2 d t I=2 [ ⁻¹ t ]₀^1= ^2 2

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