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AP EAMCET202318 May 2023Morning ShiftMathematicsIndefinite IntegrationActual

If I_n= ^n x d x(n>1) , then I₄+I₆=

Options

  1. A1 5 ^5 x+C
  2. B- 1 5 ^5 x+C
  3. C1 10 ^5 x+C
  4. D- 1 10 ^5 x+C

Correct answer

A. 1 5 ^5 x+C

Step-by-step solution

^n x d x aligned & I₄+I₆= ^4 x d x+ ^6 x d x & = ( ^4 x+ ^6 x ) d x= ^4 x ^2 x d x aligned Let x=t ^2 x d x=d t I ₄+ I ₆= t ^4 dt = t ^5 5 + C I ₄+ I ₆= 1 5 ^5 x + C

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