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A manufacturer of corrugated metal roofing wants to produce panels that are 28 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. Verify that the sine curve has equation y=sin(πx/7)y=\sin (\pi x / 7) and find the width ww of a flat metal sheet that is needed to make a 28-inch panel. (Use your calculator to evaluate the integral correct to four significant digits.)


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We can verify that the since curve has the equation sin(πx7)sin(\dfrac{\pi x}{7}) because sine oscillates between -1 and 1 for a net height of 2. This matches the metals total height.

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