JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

_ 0 ^ 64 x^ 1 3 \, dx = 3 4 [ x^ 4 3 ]_ 0 ^ 64 = 192 & _ 0 ^ 64 [x^ 1/3 ] \, dx = _ 0 ^ 1 [x^ 1/3 ] \, dx + _ 1 ^ 8 [x^ 1/3 ] \, dx + _ 8 ^ 27 [x^ 1/3 ] \, dx + _ 27 ^ 64 [x^ 1/3 ] \, dx = 156 So = 192 - 156 = 36 Now E = 1 _ 0 ^ 36 ^2 ^6 + ^6 \, d = 36 _ 0 ^ ^2 ^6 + ^6 \, d E = 36 2 _ 0 ^ /2 ^2 ^6 + ^6 \, d Let J = _ 0 ^ /2 ^2 ^6 + ^6 \, d ....(1) Applying King J = _ 0 ^ /2 ^2 ^6 + ^6 \, d .....(2) Now 2J = _ 0 ^ /2 1 ^6 + ^6 \, d (add (1) & (2)) = _ 0 ^ /2 ^6 ^6 + 1 \, d = _ 0 ^ (1 + ^2) ^4 - ^2 + 1 \, d = _ 0 ^ 1 + 1 ^2 ^2 - 1 + 1 ^2 \, d = J = 2 E = 36 2 J = 36