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Offline Centres

A region in the $x y$ plane is bounded by the graph of $y = \frac{1}{x}$ , the $x$ -axis, the line $x = m$ , and the line
$x = 2 m, m > 0$ . The area of this region

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is independent of $m$

increases as $m$ increases

decreases as $m$ increases

decreases as $m$ increases when $m < \frac{1}{2}$ and increases as $m$ increases when $m > \frac{1}{2}$

answer is A.

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Detailed Solution

$= \int_{m}^{2 m} \frac{1}{x} d x = {\ln x|}_{m}^{2 m}$

$= \ln (2 m) - \ln (m) = \ln 2$ , so the area is independent of $m$ .

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