The area bounded by x-axis, the curve y = f(x) and the lines x = 1, y = b is equal to √(b^2 + 1) - √2 for all b > 1, then f(x) is
- A. √(x - 1)
- B. √(x + 1)
- C. √(x^2 - 1)
- D. x/√(1 + x^2)
Answer: D. x/√(1 + x^2)
Explanation: By Leibniz rule, differentiating the area function ∫_1^b f(x) dx = √(b² + 1) - √2 with respect to b yields f(b) = b / √(b² + 1), so f(x) = x / √(1 + x²).