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AP EAMCET202124 Aug 2021Evening ShiftMathematicsIndefinite IntegrationActual

If 3 x-2 x 4 x+5 x d x=A |5 x+4 x|+B x+c , then A and B are

Options

  1. AA= 22 41 and B= -7 41
  2. BA= -22 41 and B= 7 41
  3. CA= -22 41 and B= -7 41
  4. DA= 22 41 and B= 7 41

Correct answer

D. A= 22 41 and B= 7 41

Step-by-step solution

We have, 3 x-2 x 4 x+5 x d x=A (5 x+4 x)+B x+c On differentiating both sides, we get 3 x-2 x 4 x+5 x = A(-5 x+4 x) 4 x+5 x +B 3 x-2 x 4 x+5 x = -5 A x+4 A x+4 B x+5 B x 4 x+5 x 3 x-2 x=(4 B-5 A) x+(5 B+4 A) x Equating the coefficient of x and x , we get 5 B+4 A=3 and 5 A-4 B=2 Solving, we get A= 22 41 and B= 7 41

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