Mathematics - Area Under Curves Question with Solution | TestHub

Required area is shaded. $$\begin{array}{rl}\therefore \mathrm{A}& ={\int }_1^{\mathrm{e}}\log \mathrm{x}\mathrm{dx}={\int }_1^{\mathrm{e}}(\log \mathrm{x})(1)\mathrm{dx}\\ & =[\mathrm{x}\log (\mathrm{x}){]}_1^{\mathrm{e}}-{\int }_1^{\mathrm{e}}\frac{1}{\mathrm{x}}\times \mathrm{x}\mathrm{dx}\\ & =[\mathrm{e}(\log \mathrm{e})-0]-[\mathrm{x}{]}_1^{\mathrm{e}}=\mathrm{e}-(\mathrm{e}-1)=1\end{array}$$