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AP EAMCET202317 May 2023Morning ShiftMathematicsDefinite IntegrationActual

_ - ^ 2 x ^2( x) d x=

Options

  1. A1- 2 4
  2. B- ( 1+ 2 4 )
  3. C2-2 4
  4. D- ( 2+ 2 4 )

Correct answer

C. 2-2 4

Step-by-step solution

I= _ - ^ 2 x ^2( x) d x Let x=t - x d x=d t aligned & I = _ -1 ^0 ^2 t(-d t)=- _ -1 ^0 1 2 (1- 2 x) d x & =- 1 2 [x- 2 x 2 ]_ -1 ^0=- 1 2 [0-(-1)+ (-2) 2 ] & = 1 2 [ (2) 2 -1 ] & =- 1 2 [ (2)-2 2 ]= 2-2 4 aligned

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