BITSAT2024MathematicsDefinite IntegrationActual
₀^ d x (x^2+a^2 ) (x^2+b^2 ) is
Options
- Aa b a+b
- Ba b 2(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
Let aligned I & = ₀^ 1 (x^2+a^2 ) (x^2+b^2 ) d x I & = 1 a^2-b^2 ₀^ (x^2+a^2 )- (x^2+b^2 ) (x^2+a^2 ) (x^2+b^2 ) d x I & = 1 a^2-b^2 ₀^ 1 (x^2+b^2 ) - 1 (x^2+a^2 ) d x I & = 1 a^2-b^2 [ 1 b ⁻¹ x b - 1 a ⁻¹ x a ]₀^ I & = 1 a^2-b^2 [ 1 b 2 - 1 a 2 ] I & = 1 (a+b)(a-b) [ a-b a b ] 2 I & = 2 a b(a+b) aligned