NDA 2025 · PYQ · Definite integral / Greatest integer function · medium
Let f(x) = [x²], where [·] is the greatest integer function. What is ∫_{√2}^{√3} f(x) dx equal to?
- A.√3 − √2✓ Correct
- B.2(√3 − √2)
- C.3 − √2
- D.1
For x ∈ [√2, √3], x² ∈ [2, 3], so [x²] = 2 (and equals 3 only at x = √3). Hence ∫_{√2}^{√3} [x²] dx = 2(√3 − √2).
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