AP EAMCET2013MathematicsIndefinite Integration
If x- x 1+ x d x=x ( x 2 )+p | ( x 2 ) |+C, then p is equal to
Options
- A-4
- B4
- C2
- D-2
Correct answer
A. -4
Step-by-step solution
Let aligned I & = x- x 1+ x d x & = x 1+ x d x- x 1+ x d x & = 1 2 x ^2 ( x 2 ) d x- 2 ( x 2 ) ( x 2 ) 2 ^2 ( x 2 ) d x & = 1 2 x ^2 ( x 2 ) d x- ( x 2 ) d x & = 1 2 x 2 ( x 2 )- 2 ( x 2 ) d x & =x x 2 - x 2 d x- ( x 2 )+C & =x x 2 -4 | x 2 |+C aligned but given, x- x 1+ x d x=x x 2 +p | x 2 |+C On comparing, we get p=-4