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MHT CET20243 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

The value of x d x is equal to

Options

  1. Ax -2 x x +c , where c is a constant of integration.
  2. B2 x -2 x x + c , where c is a constant of integration.
  3. Cx -2 x x + c , where c is a constant of integration.
  4. D2 x -2 x x + c , where c is a constant of integration.

Correct answer

D. 2 x -2 x x + c , where c is a constant of integration.

Step-by-step solution

array ll & I= x ~d x & Let x = t & 1 2 x ~d x= dt & d x=2 x dt =2 tdt & I = t 2 t dt = & 2 t tdt array aligned & =2 [ t t d t- ( d dt t t ) dt ] & =2 [ t (- t)- (- t ) dt ] & =2 [- t t+ tdt ] & =-2 t t+2 t+c & =2 x -2 x x +c aligned

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