BITSAT Mathematics Question (2024) — Solution

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