Question

The table below gives values of f(x,y), the number of milligrams of mosquito larvae per square meter in a swamp.. x=0x=2x=4. y=0136. y=3259. y=64814. If x and y are in meters and R is the rectangle 0≤x≤4, 0≤y≤6, estimate ∫Rf(x,y)dA.. . ∫Rf(x,y)dA≈ . (Include units in your answer.) . Hint: Evaluate the Riemann sums using the lower left corners and upper right corners. Then take the average of the two Riemann sums..

Answer 1

We are given with the following data. We are asked to determine the area of the object plotted. In this case, we can use average the polygons that are recognizable:

upper sum = (5 + 9 + 15 + 9)(12) = 456
lower sum = (1 + 2 + 5 + 3)(12) = 132

The average is 0.5*(456+132) = 294 units^2

This is just an approximation