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AP EAMCET202317 May 2023Evening ShiftMathematicsIndefinite IntegrationActual

77. If 5 f(x)+3 f ( 1 x )=2- 1 x , x 0 , then ₁^2 f ( 1 x ) d x=

Options

  1. A6 2-7 32
  2. B6 2-17 32
  3. C6 2-1 32
  4. D6 2-7 16

Correct answer

A. 6 2-7 32

Step-by-step solution

5 f(x)+3 f ( 1 x )=2- 1 x ...(i) Put x= 1 x in above equation: 5 f ( 1 x )+3 f(x)=2-x ...(ii) Equation (ii) 5- (i) 3 : aligned & 16 f ( 1 x )=10-5 x-6+ 3 x & f ( 1 x )= 1 16 [4-5 x+ 3 x ] aligned = 1 16 [4 x- 5 x^2 2 +3 x ]₁^2= 6 2-7 32

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