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AP EAMCET202125 Aug 2021Morning ShiftMathematicsIndefinite IntegrationActual

If 2 x+3 x 4 x+5 x d x= ( 23 41 ) x+K |4 x+5 x|+c , then K is equal to

Options

  1. A2 41
  2. B-2 41
  3. C3 41
  4. D-3 41

Correct answer

B. -2 41

Step-by-step solution

We have, aligned 2 x+3 x 4 x+5 x & = 23 41 x & +K |4 x+5 x|+C aligned On differentiating, we get aligned & 2 x+3 x 4 x+5 x = 23 41 + K(-4 x+5 x) 4 x+5 x & 2 x+3 x &= 92 x+115 x-164 K x+205 K x 41 & 2 x+3 x= ( 92+205 K 41 ) x &+ ( 115-164 K 41 ) x aligned Equating the coefficient of x and x , we get aligned 92+205 K 41 & =2 and 115-164 K 41 =3 92+205 K & =82 K & = -10 205 = -2 41 aligned

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