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AP EAMCET202018 Sep 2020Evening ShiftMathematicsDefinite IntegrationActual

( ₀^ / 4 ( ^2 x- ^4 x ) d x= )

Options

  1. A3
  2. B2
  3. C( 1 3 )
  4. D0

Correct answer

C. ( 1 3 )

Step-by-step solution

( aligned & ₀^ 4 ( ^2 x+ ^4 x ) d x & ₀^ 4 (1+ ^2 x ) ^2 x d x & ₀^ 4 ^2 x ^2 x d x & Put, x=t & ^2 x d x=d t aligned ) when (x= 4 ), then (t=1 ) and when (x=0 ), then (t=0 ) (= ₀^1 t^2 d t= ( t^3 3 )₀^1= ( 1 3 -0 )= 1 3 ) Hence, option (c) is correct.

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