The area bounded by the coordinate axes and normal to the curve $y=\log _e x$ at the point P(1, 0), is

1 sq. unit 2 sq. units $\frac{1}{2}$ sq. unit none of these

$\frac{1}{2}$ sq. unit

We have, $y=\log _e x \Rightarrow \frac{d y}{d x}=\frac{1}{x} \Rightarrow\left(\frac{d y}{d x}\right)_P=1$ The equation of the normal at (1, 0) is $y-0=-1(x-1) \Rightarrow x+y=1$ Clearly, it makes a triangle of area $\frac{1}{2}$ sq. unit with the coordinate axes.