Question
Let [ ] denote the greatest integer function. Then _ - 2 ^ 2 ( 12(3+[x]) 3+[ x]+[ x] ) d x is equal to :
JEE Main
Mathematics
Definite Integration
2026
JEE Main 2026 (28 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 13 +1
- B. 12 +5
- C. 11 +2
- D. 15 +4
Answer
C. 11 +2
Step-by-step solution
I = _ - /2 ^ /2 12(3 + [x]) \, dx 3 + [ x] + [ x] I = _ - /2 ^ -1 12(1) \, dx 2 + _ -1 ^ 0 12(2) \, dx 2 + _ 0 ^ 1 12(3) \, dx 3 + _ 1 ^ /2 12(4) \, dx 3 I = 6 ( 2 - 1 ) + 12(0 + 1) + 12(1 - 0) + 16 ( 2 - 1 ) I = 3 - 6 + 12 + 12 + 8 - 16 I = 11 + 2
Related: Mathematics — Definite Integration · All PYQ Banks