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MHT CET202312 May 2023Morning ShiftMathematicsIndefinite IntegrationActual

cosec x ~d x ^2 (1+ x 2 ) =

Options

  1. A(1+ ( x 2 ) )+ c , where c is constant of integration
  2. B(1+ ( x))+ c , where c is constant of integration
  3. C( ( x 2 ) )+ c , where c is constant of integration.
  4. D( x 2 )+c , where c is constant of integration.

Correct answer

A. (1+ ( x 2 ) )+ c , where c is constant of integration

Step-by-step solution

Let I = cosec x ~d x ^2 (1+ x 2 ) d x Let 1+ ( x 2 )= t Differentiating both sides w.r.t. t, we get aligned & 1 x 2 ^2 x 2 1 2 ~d x= dt & 1 2 x 2 x 2 ~d x= dt & cosec x ~d x= dt & I = 1 ^2 t dt = ^2 t d t & = ( t )+ c & = (1+ ( x 2 ) )+c & aligned

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