91Ó°ÊÓ

Irrigation Canal Gate The vertical cross section of an irrigation canal is modeled by \(f(x)=\frac{5 x^{2}}{x^{2}+4}\) where \(x\) is measured in feet and \(x=0\) corresponds to the center of the canal. Use the integration capabilities of a graphing utility to approximate the fluid force against a vertical gate used to stop the flow of water if the water is 3 feet deep.

Let \(V\) be the region in the cartesian plane consisting of all points \((x, y)\) satisfying the simultaneous conditions \(|x| \leq y \leq|x|+3\) and \(y \leq 4\) Find the centroid \((\bar{x}, \bar{y})\) of \(V\).