Question: A barn is 100 feet long and 40 feet wide. A cross section of the barn’s roof is the inverted caternary \(y\quad =\quad 31\quad -\quad 10\,\left( {{e}^{{}^{\,x}\!\!\diagup\!\!{}_{20}\;}}\quad +\quad {{e}^{{}^{\,-\,x}\!\!\diagup\!\!{}_{20}\;}} \right)\) . Find the number of square feet of roofing on the barn. See the figure.