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Question #41557

Difficulty: 8/10 | 🟢 Free

The Question

Let $R$ be the region in the first quadrant bounded by the curve $y = \left[ \frac{6}{x} \right]$ , the x-axis, and the vertical lines $x = 1$ and $x = 4$ , where $[t]$ denotes the greatest integer less than or equal to $t$ . If $A$ is the area of the region $R$ , then the value of $10A$ is:

Options

A.
67
B.
60
C.
77
D.
87

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

Bounded vs Unbounded Regions|Rectangular Hyperbola|Greatest Integer Function Traps

Why This Question Is Tricky

Common Mistakes

The problem tests the student's ability to correctly partition the domain of integration when a continuous function (a rectangular hyperbola) is subjected to the Greatest Integer Function.

The primary trap lies in the final fractional segment.

Students often assume that the interval for $[6/x] = 1$ extends fully to its natural asymptote boundary at $x=6$ , erroneously adding the full block area (which would yield 87) instead of truncating it at the given upper limit $x=4$ .

Additionally, students may incorrectly partition the integral at integer values of $x$ rather than integer values of $y$ , leading to severe miscalculation of the area.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Application of Integrals - Class 12
Concept	Bounded vs Unbounded Regions
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free