BITSAT Mathematics Question (2024) — Solution

Step-by-step solution

Let I= _0^ 2 ( x) d x....(i) By applying property, aligned _a^b f(x) d x & = _a^b f(a+b-x) d x \\ I & = _0^ 2 ( ( 2 -x ) ) d x \\ I & = _0^ 2 ( x) d x (ii) aligned Adding Eqs. (i) and (ii), aligned & 2 I= _0^ 2 [ ( x)+ ( x)] d x \\ & 2 I= _0^ 2 1 d x=0 aligned