Let a be a positive constant, and let R be the triangular region with vertices (0,0),...

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Let a be a positive constant, and let R be the triangular region with vertices (0,0), (0, a), and (2a, a). (a) Sketch a picture of R. Based on the picture, do you expect the average value of f(x, y) = x on R to be less than a, equal to a, or greater than a? Explain. (b) Calculate the average value of f(x, y) = x on R. (Does your answer agree with your answer to #3(a)?) Let a be a positive constant, and let R be the triangular region with vertices (0,0), (0, a), and (2a, a). (a) Sketch a picture of R. Based on the picture, do you expect the average value of f(x, y) = x on R to be less than a, equal to a, or greater than a? Explain. (b) Calculate the average value of f(x, y) = x on R. (Does your answer agree with your answer to #3(a)?)