A manufacturer of corrugated metal roofing wants to produce panels that are u = 48 in. wide and 2 in. thick by processing flat sheets of metal as shown in the figure. The profile of the roofing takes the shape of a sine wave with equation y = sin(pi x/12). Find the width w of a flat metal sheet that is needed to make a 48-inch panel. (Use your calculator to evaluate the integral correct to four significant digits.) in.