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AP EAMCET202315 May 2023Morning ShiftMathematicsIndefinite IntegrationActual

If ( 4 e^x+6 e^ -x 9 e^x-4 e^ -x ) d x=A x+B | (9 e^ 2 x -4 ) |+C , then ( A , B )=

Options

  1. A( 3 2 , 35 36 )
  2. B( -3 2 , -35 36 )
  3. C( -3 2 , 35 36 )
  4. D( 3 2 , -35 36 )

Correct answer

B. ( -3 2 , -35 36 )

Step-by-step solution

Let I= 4 e^x+6 e^ -x 9 e^x-4 e^ -x d x= 4 e^ 2 x +6 9 e^ 2 x -4 d x Let 4 e^ 2 x +6=A (9 e^ 2 x -4 )+B (18 e^ 2 x )4 e^ 2 x +6=(9 A+18 B) e^ 2 x -4 A Comparing both sides we get, A=- 3 2 , B= 35 36 aligned & I=- 3 2 (9 e^ 2 x -4 ) d x (9 e^ 2 x -4 ) + 35 36 18 e^ 2 x 9 e^ 2 x -4 d x & I=- 3 2 d x+ 35 36 18 e^ 2 x 9 e^ 2 x -4 d x & I=- 3 2 + 35 36 | (9 e^ 2 x -4 ) |+c & Hence A=- 3 2 , B= 35 36 aligned

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