Find the average value of the function $f\left(x\right)=\sin x$ on the interval $[0,\pi ]$.

A tunnel is shaped in a form of a parabola with a base width of $800\text{ ft}$ and a maximum height of $600\text{ ft}$. Its cross-section can be modeled by $y=600(1-{\left(\frac{x}{400}\right)}^2)$. What is the average height of the tunnel above the ground?

Let $g^{\prime }\left(x\right)$ be continuous for all real $x$. What is the average value of $g^{\prime }\left(x\right)$ on the interval $[2,7]$?