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AP EAMCET20228 Jul 2022Evening ShiftMathematicsDefinite IntegrationActual

₀^ (x¹²+x⁻¹² ) x x d x=

Options

  1. A0
  2. B1
  3. C2
  4. De^2

Correct answer

A. 0

Step-by-step solution

I= ₀^ (x¹²+x⁻¹² ) x x d x Put t= 1 x d t=- 1 x^2 d x -x d t= 1 x d x - d t t = 1 x d x I= _ ^0 (t⁻¹²+t¹² )(- t) ( -d t t ) aligned & = _ ^0 (t⁻¹²+t¹² ) ( t t ) d t & =- ₀^ (t⁻¹²+t¹² ) ( t t ) d t aligned aligned I & =- ₀^ (x⁻¹²+x¹² ) ( x x ) d x 2 I & =0 I=0 aligned

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