Question
_ 0 ^ dx ( x ^ 2 + a ^ 2 ) ( x ^ 2 + b ^ 2 ) is
BITSAT
Mathematics
Definite Integration
2020
BITSAT 2020
BITSAT Mathematics Question (2020) — Solution
Options
- A. a b a+b
- B. 2(a+b)
- C. 2 a b(a+b)
- D. (a+b) 2 a b
Answer
C. 2 a b(a+b)
Step-by-step solution
_ 0 ^ d x (x^ 2 +a^ 2 ) (x^ 2 +b^ 2 ) = 1 b^ 2 -a^ 2 _ 0 ^ (x^ 2 +b^ 2 )- (x^ 2 +a^ 2 ) (x^ 2 +a^ 2 ) (x^ 2 +b^ 2 ) = 1 b^ 2 -a^ 2 _ 0 ^ [ 1 x^ 2 +a^ 2 - 1 x^ 2 +b^ 2 ] d x = 1 b^ 2 -a^ 2 [ 1 a ^ -1 x a - 1 b ^ -1 x b ]_ 0 ^ = 1 b^ 2 -a^ 2 [ 2 a - 2 b ]= 2 a b(a+b)
Related: Mathematics — Definite Integration · All PYQ Banks