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AP EAMCET202125 Aug 2021Evening ShiftMathematicsIndefinite IntegrationActual

If 1+ (4 x) (x)- (x) d x=A (4 x)+B , then A is equal to

Options

  1. A-1 2
  2. B-1 4
  3. C-1 3
  4. D-1 8

Correct answer

D. -1 8

Step-by-step solution

1+ (4 x) x- x d x=A (4 x)+B , then A= ? Let aligned I & = 1+ (2 2 x) x- x d x= 1+2 ^2(2 x)-1 x x - x x d x & = 2 ^2(2 x) ^2 x- ^2 x ( x x) d x I & =2 ^2 2 x 2 x ( x x) d x aligned aligned I & = (2 x)( 2 x) d x & = 1 2 2 (2 x) (2 x) d x= 1 2 4 x d x I & = - 4 x 8 +C=k (4 x)+C k & =- 1 8 aligned

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