Let R be the rectangle with vertices (0,0), (2,0), (2,2), and (0,2) and let f(x,y)=sqrt(xy) (a) Find reasonable upper and lower bounds for ∫RfdA without subdividing R. upper bound =  lower bound =  (b) Estimate ∫RfdA three ways: by partitioning R into four subrectangles and evaluating f at its maximum and minimum values on each subrectangle, and then by considering the average of these (over and under) estimates. overestimate: ∫RfdA≈  underestimate: ∫RfdA≈ average: ∫RfdA≈

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