BITSAT2020MathematicsDefinite IntegrationActual
₀^ dx ( x ²+ a ² ) ( x ²+ b ² ) is
Options
- Aa b a+b
- B2(a+b)
- C2 a b(a+b)
- D(a+b) 2 a b
Correct answer
C. 2 a b(a+b)
Step-by-step solution
₀^ d x (x²+a² ) (x²+b² ) = 1 b²-a² ₀^ (x²+b² )- (x²+a² ) (x²+a² ) (x²+b² ) = 1 b²-a² ₀^ [ 1 x²+a² - 1 x²+b² ] d x= 1 b²-a² [ 1 a ⁻¹ x a - 1 b ⁻¹ x b ]₀^ = 1 b²-a² [ 2 a - 2 b ]= 2 a b(a+b)