The area of the region bounded by y = log x, y = 2 and the coordinate axes is

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The area of the region bounded by $y = \log x, y = 2$ and the coordinate axes is

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$e^{2} - 2$

$e^{2} - 1$

$e^{2} - e$

$e^{2} + 1$

answer is B.

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Detailed Solution

Required area = area of rectangle $O A B C -$ area under $y = \log x, x = 1, x = e^{2}$
$\begin{array}{l} = A O \times O C - \int_{1}^{e^{2}} \log x d x \\ = 2 e^{2} - [x \log x - x]_{1}^{2} \\ = 2 e^{2} - [2 e^{2} - e^{2}] - 1 = e^{2} - 1 . \end{array}$