a. Values of f(x,y) are in the table below. Let R be the rectangle 1 ≤ x ≤ 1.2, 2 ≤ y ≤ 2.4. Find the Riemann sum which is a reasonable over estimate for ∫Rf(x,y) dA with Δx=0.1 and Δy=0.2. Show what you calculate.
|
|
x
|
|
1.0
|
1.1
|
1.2
|
|
y
|
2.0
|
5
|
7
|
10
|
|
2.2
|
4
|
6
|
8
|
|
2.4
|
3
|
5
|
4
|
b. Referring to the problem above, if R is a rectangular plate, x and y are distances measured in millimeters and f(x,y) is the density of bacteria per square millimeter what would the integral represent?