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AP EAMCET202419 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

Let f(x)= x (x^2+1 ) (x^2+3 ) d x . If f(3)= 1 4 ( 5 6 ) then f(0)=

Options

  1. A1 4 ( 1 3 )
  2. B0
  3. C1 2 ( 1 3 )
  4. D( 1 3 )

Correct answer

A. 1 4 ( 1 3 )

Step-by-step solution

f(x)= x (x^2+1 ) (x^2+3 ) d x Let x^2=t 2 x d x=d t aligned & So, f(x)= 1 2 d t (t+1)(t+3) & = 1 4 ( 1 t+1 - 1 t+3 ) d t= 1 4 ( 1+x^2 3+x^2 )+c aligned aligned & Since, f(3)= 1 4 ( 5 6 ) 1 4 ( 5 6 ) & = 1 4 ( 10 12 )+c c=0 & f(x)= 1 4 ( 1+x^2 3+x^2 ) So, f(0)= 1 4 ( 1 3 ) aligned

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