The area of the region bounded by the curve $y=\log x, x$ -axis and the lines $x=1, x=e$ is
The area of the region bounded by the curve $y=\log x, x$ -axis and the lines
$x=1, x=e$ is
- $\frac{1}{e}$ Sq. Units
- 1 Sq. Units
- 4 sq. Units
- $\frac{1}{2}$ Sq. Units
Solution
Required area is shaded.
$\begin{aligned}
\therefore \mathrm{A} &=\int_{1}^{\mathrm{e}} \log \mathrm{x} \mathrm{dx}=\int_{1}^{\mathrm{e}}(\log \mathrm{x})(1) \mathrm{dx} \\
&=[\mathrm{x} \log (\mathrm{x})]_{1}^{\mathrm{e}}-\int_{1}^{\mathrm{e}} \frac{1}{\mathrm{x}} \times \mathrm{x} \mathrm{dx} \\
&=[\mathrm{e}(\log \mathrm{e})-0]-[\mathrm{x}]_{1}^{\mathrm{e}}=\mathrm{e}-(\mathrm{e}-1)=1
\end{aligned}$
Asked in: MHT CET 2020 (14 Oct Shift 1)
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