Values of f(x,y) are given in the table below. Let R be the rectangle 1≤x≤1.6, 2≤y≤3.2. Find a Riemann sum which is a reasonable estimate for ∫Rf(x,y)da with Δx=0.2 and Δy=0.4. Note that the values given in the table correspond to midpoints.

Question

--------------x=1.1 --- x=1.3 --- x=1.5
y=2.2-----6 ----------6---------10
y=2.5-----8----------(-5)---------2
y=3-----(-5)-----------3---------10

Answer 1

this is just like the Riemann sum for f(x).
You have 9 rectangles, each of area 0.2 * 0.4 = 0.8
So add up 0.8 * f(x,y) at each of the given midpoints.

Answer 2

0.2*0.4 = 0.08 then u should get the right answer