A manufacturer of corrugated metal roofing wants to produce panels that are u = 36 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(x/9).
Find the width w of a flat metal sheet that is needed to make a 36-inch panel. (Use your calculator to evaluate the integral correct to two decimal places.)