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AP EAMCET202125 Aug 2021Morning ShiftMathematicsIndefinite IntegrationActual

If 5 (x) (x)-2 d x=x+a | (x)-2 (x)|+k , then a is equal to

Options

  1. A-1
  2. B-2
  3. C1
  4. D2

Correct answer

D. 2

Step-by-step solution

We have, 5 x x-2 d x=x+a | x-2 x|+K On differentiating, we get aligned & 5 x x-2 =1+ a( x+2 x) x-2 x 5 x x-2 & =1+ a(1+2 x) x-2 & 5 x x-2 = x-2+a+2 a x x-2 5 x & =(2 a+1) x+a-2 aligned Equating the coefficient of x and constant terms, we get aligned 2 a+1 & =5 a-2 & =0 a & =2 aligned

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