A sine curve

$\large \displaystyle \bar{y} = \frac{\int_0^{\pi} \frac12 \sin(x)^2 dx }{\int_0^{\pi} \sin(x) dx}$

$\large \displaystyle \bar{y} = \frac{\int_0^{\pi} \frac14 [1 - \cos(2x)] dx }{- \cos(x) \Big | _0^{\pi} }$

$\large \displaystyle \bar{y} = \frac{(\frac{x}{4} - \frac{\sin(2x)}{8}) \Big | _0^{\pi} }{2}$

$\large \displaystyle \color{#3D99F6} \bar{y} = \frac{\pi}{8} \approx \fbox{0.3926...}$