Given f x cos x and g x cos x give exact answers for all parts a Plot the functions on the x interval 0 5 Find the volume when the region between the two curves is rotated about the line x b Find the area of the region 1 x f x g x dx A a cb 1 1 and y I x g x dx with A the area between the curves Find the x A coordinate of the center of mass of the region In a print statement explain why this answer makes sense based on the graph in part a c The center of mass of a region a b is the point x y where cb d When the region rotates about the line x how far does the center of mass travel Multiply this value by the area What do you notice when you compare your answer to part a