The area bounded by the curve y = log x, y = 0 and x = e , is

The correct answer is Option (3) → 1 sq. units

The curve \(y = \log x\) meets the x-axis at x = 1 and lies above it for \(1 \lt x \le e\). So the region runs from x = 1 to x = e, and by integration by parts, \(\int \log x\,dx = x\log x - x\):

    \(\displaystyle \text{Area} = \int_{1}^{e} \log x\,dx = \Big[x\log x - x\Big]_{1}^{e}\)

    \(= (e \cdot 1 - e) - (1 \cdot 0 - 1)\)
    \(= 0 + 1 = 1\) sq. unit