JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

Let I_r = _ 0 ^ r x| x| \, dx .....(1) Apply King Property = _ 0 ^ r (r - x)| x| \, dx .....(2) By (1) + (2) 2I_r = _ 0 ^ r r| x| \, dx I_r = r 2 _ 0 ^ r | x| \, dx I_1 = 1 2 _ 0 ^ 1 | x| \, dx = 1 2 _ 0 ^ | t| \, dt = 1 2 (2) I_2 = 2 2 _ 0 ^ 2 | x| \, dx = 2 2 _ 0 ^ 2 | t| \, dt = 2 2 (4) S = 1 2 2 + 2 2 4 + 3 2 6 + + 20 2 (2 20) = 1 + 2 + 3 + + 20 = 20 21 2 = 210