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MHT CET20242 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

x 3 x ~d x is equal to

Options

  1. A1 3 ( x )+ c , (where c is a constant of integration)
  2. B2 3 ( x )^2+ c , (where c is a constant of integration)
  3. C2 3 ( x)^2+ c , (where c is a constant of integration)
  4. D1 12 ( x)^2+ c ,( where c is a constant of integration)

Correct answer

D. 1 12 ( x)^2+ c ,( where c is a constant of integration)

Step-by-step solution

aligned & Put x= t ^2 ~d x=2 tdt & aligned x 3 x ~d x & = t 3 t ^2 (2 tdt ) & = 2 3 t t dt & = 2 3 ( t )^2 2 + c = ( x )^2 3 + c & = 1 3 ( 1 2 x )^2+ c & = 1 12 ( x)^2+ c aligned aligned

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