Question
Consider the following for the two (02) items that follow: Let f(x) = [x^2], where [ ] is the greatest integer function. What is _ 2 ^ 3 f(x) \, dx equal to?
NDA
Mathematics
Area Under Curves
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 3 - 2
- B. 2( 3 - 2 )
- C. 3 - 2
- D. 1
Answer
B. 2( 3 - 2 )
Step-by-step solution
Given f(x) = [x^2]. The limits of integration are from x = 2 to x = 3 . For x ( 2 , 3 ), the value of x^2 lies in the interval (2, 3). Therefore, the greatest integer function [x^2] = 2. The integral is given by: _ 2 ^ 3 f(x) \, dx = _ 2 ^ 3 [x^2] \, dx = _ 2 ^ 3 2 \, dx = 2[x]_ 2 ^ 3 = 2( 3 - 2 )
Related: Mathematics — Area Under Curves · All PYQ Banks