Question

Evaluate : $\stackrel{e}{\underset{1}{\int }}\frac{1}{x}dx$.

Answer 1

We need to find the value of ${\int }_1^e\frac{1}{x}dx$

We know that the differentiation of $\ln \left(x\right)$ is equal to $\frac{1}{x}$

Therefore the integration of $\frac{1}{x}$ is equal to $\ln \left(x\right)$

$⟹{\int }_1^e\frac{1}{x}dx={\left|\ln x\right|}_1^e=\ln e-\ln 1=1-0=1$

Therefore the value of ${\int }_1^e\frac{1}{x}dx$ is $1$