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AP EAMCET202315 May 2023Morning ShiftMathematicsIndefinite IntegrationActual

If f(x)= d x (x^2+2 ) and f( 2 )=0 , then f(0)=

Options

  1. A2 2
  2. B- 2 2
  3. C- 4 2
  4. D4 2

Correct answer

C. - 4 2

Step-by-step solution

f(x)= d x x^2+( 2 )^2 = 1 2 ⁻¹ ( x 2 )+c Since at x= 2 , f(x)=0 0= 1 2 ⁻¹(1)+c c=- 4 2 Hence f(0)= 1 2 ⁻¹ ( 0 2 )+ (- 4 2 )=- 4 2

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