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AP EAMCET202420 May 2024Evening ShiftMathematicsDefinite IntegrationActual

₀^ x x 1+ ^2 x d x=

Options

  1. A0
  2. B2
  3. C^2 2
  4. D^2 4

Correct answer

D. ^2 4

Step-by-step solution

I = ₀^ x x 1+ ^2 x d x .... (i) I= ₀^ ( -x) ( -x) 1+ ^2( -x) d x= ₀^ ( -x) x .1+ ^2 x ) d x .... (ii) Adding (i) and (ii), 2 I = ₀^ x 1+ ^2 x d x Let x=t - x d x=d t aligned & 2 I = _ -1 ^1 d t 1+t^2 & 2 I = [ ⁻¹(t) ]_ -1 ^1 I = ^2 4 aligned

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