Question
The value of _ - 2 ^ 2 ( 1 [x]+4 ) d x, where [ ] denotes the greatest integer function, is
JEE Main
Mathematics
Definite Integration
2026
JEE Main 2026 (22 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 1 60 (21 -1)
- B. 7 60 ( -3)
- C. 7 60 (3 -1)
- D. 1 60 ( -7)
Answer
C. 7 60 (3 -1)
Step-by-step solution
I = _ - /2 ^ /2 1 [x] + 4 \, dx I = _ - /2 ^ -1 dx 2 + _ -1 ^ 0 dx 3 + _ 0 ^ 1 dx 4 + _ 1 ^ /2 dx 5 = 1 2 (-1 + 2 ) + 1 3 (1) + 1 4 (1) + 1 5 ( 2 - 1 ) = 7 20 - 7 60 = 7 60 (3 - 1)
Related: Mathematics — Definite Integration · All PYQ Banks