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AP EAMCET202017 Sep 2020Morning ShiftMathematicsIndefinite IntegrationActual

( ^3(x) ^3(x) d x= )

Options

  1. A( ^4(x)- ^6(x)+c )
  2. B( ^4(x)- ^6(x)+c )
  3. C( 1 4 ^4(x)- 1 6 ^6(x)+c )
  4. D( 1 4 ^4(x)- 1 6 ^6(x)+c )

Correct answer

C. ( 1 4 ^4(x)- 1 6 ^6(x)+c )

Step-by-step solution

( aligned & ^3 x ^3 x d x & = ^3 x x (1- ^2 x ) d x aligned ) Let (t= x d t= x d x ) ( aligned & t^3 (1-t^2 ) d t= (t^3-t^5 ) d t & t^4 4 - t^6 6 +C= ^4 x 4 - ^6 x 6 +C aligned )

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