What is the integral from 0 to 1 of log_{e}(x) ?

The integral from 0 to 1 of log_{e}(x) is -1

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integral from 0 to 1 of log_{e}(x)

\int_{0}^{1} lo g_{e} (x) d x

- 1

Solution steps

\int_{0}^{1} lo g_{e} (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{0}^{1}

= [x ln (x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= [x ln (x) - x]_{0}^{1}

Compute the boundaries:

- 1

= - 1

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What is the integral from 0 to 1 of log_{e}(x) ?
The integral from 0 to 1 of log_{e}(x) is -1