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Question #41904

Difficulty: 8/10 | 🟢 Free

The Question

Let $F(x) = \int_{x}^{x^2} [|273 - 90t|] \, dt$ , where $[ \cdot ]$ denotes the greatest integer function. Find the value of $F'(2^+) - F'(2^-)$ .

Options

A.
5
B.
-5
C.
0
D.
3

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

Modulus Function Breakdown|Newton-Leibniz Formula with variable limits|Fundamental Theorem of Calculus|Integral Part and Fractional Part

Why This Question Is Tricky

Common Mistakes

This question tests the application of the Newton-Leibniz formula on an integral with variable limits where the integrand contains jump discontinuities.

The primary trap is the incorrect assumption that continuity of the integral implies differentiability, leading students to directly plug in integer values (yielding 0).

Furthermore, the nested modulus reverses the directional limit for negative arguments (e.g., as $t \to 4^+$ , the inner expression becomes more negative, but its modulus approaches 87 from above), creating a severe trap for sign errors and incorrect GIF evaluations.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Continuity and Differentiability - Class 12
Concept	Modulus Function Breakdown
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free