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BITSAT2021MathematicsIndefinite IntegrationActual

The value of ( x) d x is :

Options

  1. A1 2 [ ( x)+ ( x)]+C
  2. Bx 2 [ ( x)+ ( x)]+C
  3. Cx 2 [ ( x)- ( x)]+C
  4. D1 2 [ ( x)- ( x)]+C

Correct answer

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

Step-by-step solution

Let ( I = ( x ) 1 ~d x . . (i) ) Use integral by parts, ( aligned &I= ( x) x- [- ( x)] 1 x x d x &=x ( x)+ ( x) 1 d x &=x ( x)+ [ ( x) x- ( x) 1 x x d x ]+C &=x ( x)+ [x ( x)- ( x) d x ]+C &=x ( x)+ ( x) -I+C[f r o m Eq. (i) ] & I= x 2 ( x)+ ( x) +C aligned )

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