Question

Find the area bounded by the curve $y=\log x$, x-axis and the ordinates $x=1$ and $x=e$

Answer 1

Area $={\int }_1^e\ln xdx$

$={[x\ln x-x]}_1^e$

$=(e\ln e-e)-(1\ln 1-1)$

$=(e-e)+1$

$=1$