Question
The value of ( x) d x is :
BITSAT
Mathematics
Indefinite Integration
2021
BITSAT 2021
BITSAT Mathematics Question (2021) — Solution
Options
- A. 1 2 [ ( x)+ ( x)]+C
- B. x 2 [ ( x)+ ( x)]+C
- C. x 2 [ ( x)- ( x)]+C
- D. 1 2 [ ( x)- ( x)]+C
Answer
B. x 2 [ ( x)+ ( x)]+C
Step-by-step solution
Let \( I = ( x ) 1 ~d x . . (i) \) Use integral by parts, \( aligned &I= ( x) x- [- ( x)] 1 x x d x \\ &=x ( x)+ ( x) 1 d x \\ &=x ( x)+ [ ( x) x- ( x) 1 x x d x ]+C \\ &=x ( x)+ [x ( x)- ( x) d x ]+C \\ &=x\ ( x)+ ( x)\ -I+C[f r o m Eq. (i) ] \\ & I= x 2 \ ( x)+ ( x)\ +C aligned \)
Related: Mathematics — Indefinite Integration · All PYQ Banks