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MHT CET2012MathematicsIndefinite Integration

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 [ from Eq. (i) ] & I= x 2 ( x)+ ( x) +C aligned

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