NDA Mathematics Question (2026) — Solution

Step-by-step solution

Given k = _0^ 2 a x+b x (a+b)( x+ x) \,dx Multiplying both sides by (a+b): k(a+b) = _0^ 2 a x+b x x+ x \,dx Using the definite integral property _0^a f(x)\,dx = _0^a f(a-x)\,dx, replacing x with 2 -x: k(a+b) = _0^ 2 a ( 2 -x )+b ( 2 -x ) ( 2 -x )+ ( 2 -x ) \,dx k(a+b) = _0^ 2 a x+b x x+ x \,dx This matches the required integral. Thus, the value is k(a+b). Answer: k(a+b)