mathimatikoi.org

Find the geometric mean , with respect to the usual measure on the interval, of all the real numbers in the range $(0, 1]$.

Nice one. The geometric mean with respect to the usual measure on the interval is actually defined as:

$$\mathcal{GM} = e^{\displaystyle \int_{0}^{1} \ln x \, dx} = e^{-1} = \frac{1}{e}$$

and this is our answer.