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AP EAMCET201921 Apr 2019Morning ShiftMathematicsIndefinite IntegrationActual

aligned & If x 2 x 5 x d x & =A 2 x+B 4 x+C 6 x+D 8 x+k aligned (where k is the arbitrary constant of integration), then 1 B + 1 C =

Options

  1. A1 A - 1 D
  2. B1 A + 1 D
  3. C1
  4. D0

Correct answer

B. 1 A + 1 D

Step-by-step solution

Given, aligned x & 2 x 5 x d x & = 1 2 2 x 5 x 2 x d x & = 1 2 (5 x+x)+ (5 x-x) 2 x d x & = 1 2 ( 6 x+ 4 x) 2 x d x & = 1 4 (2 6 x 2 x+2 2 x 4 x) d x & = 1 4 ( 8 x+ 4 x+ 6 x+ 2 x) d x & = 1 4 [ 8 x 8 + 4 x 4 + 6 x 6 + 2 x 2 ]+k & = 2 x 8 + 4 x 16 + 6 x 24 + 8 x 32 +k aligned On comparing, aligned A & = 1 8 , B= 1 16 , C= 1 24 and D= 1 32 1 B + 1 C & =16+24=40 aligned Now, 1 A + 1 D =8+32=40 1 B + 1 C = 1 A + 1 D

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