What is the integral from e to 1 of 1/x ?

The integral from e to 1 of 1/x is -1

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integral from e to 1 of 1/x

\int_{e}^{1} \frac{1}{x} d x

- 1

Solution steps

\int_{e}^{1} \frac{1}{x} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{e} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - [ln ∣ x ∣]_{1}^{e}

Compute the boundaries:

1

= - 1

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