NDA Mathematics Question (2026) — Solution

Step-by-step solution

Let I = _0^ 2 a x+b x (a+b)( x+ x) \,dx Using the property _0^a f(x)\,dx = _0^a f(a-x)\,dx, we get: I = _0^ 2 a ( 2 -x )+b ( 2 -x ) (a+b) ( ( 2 -x )+ ( 2 -x ) ) \,dx I = _0^ 2 a x+b x (a+b)( x+ x) \,dx Adding the two equations for I, we get: 2I = _0^ 2 a x+b x+a x+b x (a+b)( x+ x) \,dx 2I = _0^ 2 (a+b)( x+ x) (a+b)( x+ x) \,dx 2I = _0^ 2 1 \,dx 2I = 2 I = 4 Thus, k = 4 Answer: 4