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Question #40341

Difficulty: 8/10 | 🟢 Free

The Question

Let $F(x) = \int_{x}^{x^2} \frac{dt}{\sqrt{3 - |[t]|}}$ , where $[t]$ denotes the greatest integer less than or equal to $t$ . Let $D$ be the maximal domain of $F(x)$ in $\mathbb{R}$ , and $S$ be the set of points in $D$ where $F(x)$ is not differentiable. Find the number of elements in $S$ .

Options

A.
3
B.
4
C.
5
D.
6

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Monster

Ultra-high difficulty questions designed to test your limit, stamina, and deep conceptual understanding.

Concepts Behind This Question

Real-Valued Function Domain|Newton-Leibniz Formula with variable limits|Greatest Integer Function Traps|Compound Function Boundaries

Why This Question Is Tricky

Common Mistakes

This question tests the lethal collision between the Newton-Leibniz formula and piecewise constant functions (like the Greatest Integer Function).

A common trap is blindly applying the Leibniz rule to find $F'(x)$ without realizing that the fundamental theorem of calculus requires the integrand to be continuous at the variable limits.

If the limits cross a discontinuity of the integrand, the derivative of the integral experiences a jump, leading to non-differentiability.

Furthermore, the problem embeds a nested domain constraint, forcing students to ensure the entire interval of integration lies within the integrand's domain, not just the endpoints.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Relations and Functions - Class 11
Concept	Real-Valued Function Domain
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free