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MHT CET202211 Aug 2022Morning ShiftMathematicsDefinite IntegrationActual

The value of ( _e(x) ) d x is equal to (where C is a constant of integration.)

Options

  1. Ax[ ( x)- ( x)]+C
  2. Bx 2 [ ( x)- ( x)]+C
  3. Cx 2 [ ( x)+ ( x)]+C
  4. Dx[ ( x)+ ( x)]+C

Correct answer

C. x 2 [ ( x)+ ( x)]+C

Step-by-step solution

aligned & ( _ e x ) d x let _ _ e x=t & d x=e^t & I= t e^t ~d t= t e^t+ t e^t-I [ Integrating by parts] & 2 I=e^t( t+ t) & I= x 2 ( _ e x )+ ( _ e x ) aligned

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