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BITSAT2009MathematicsIndefinite IntegrationActual

If ( 2 x- x+ x+ x-2 d x ) (=A | x+ x-2|+B x+C ). Then the ordered triplet (A, B, ) is -

Options

  1. A( ( 1 2 , 3 2 ,-1 ) )
  2. B( ( 3 2 , 1 2 ,-1 ) )
  3. C( ( 1 2 ,-1, 3 2 ) )
  4. D( ( 3 2 ,-1, 1 2 ) )

Correct answer

B. ( ( 3 2 , 1 2 ,-1 ) )

Step-by-step solution

( aligned & d dx ( A | x + x -2|+ Bx + C ) &= A x - x x + x -2 + B &= A x - A x + B x + B x -2 ~B x + x -2 & 2= A + B or -1=- A + B ; =-2 ~B & A =3 / 2, ~B =1 / 2, =-1 aligned )

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