UNCLICK the orange region R but keep R's bounday, just for ease of viewing.
13
Well, let's partition the orange region R into rectangles (compare with single integral)
14
Folder 1: Partition R using (change in x) = (change in y) = 3.
Hide this folder from students.
15
UNCLICK Folder 1's icon (icon: folder in a circle).
26
Folder 2: Partition R using (change in x) = (change in y) = 3/2 = 1.5.
Hide this folder from students.
27
UNCLICK Folder 2's icon (icon: folder in a circle).
38
Folder 3: Partition R using (change in x) = (change in y) = 3/4 = 0.75
Hide this folder from students.
39
UNCLICK Folder 3's icon (icon: folder in a circle).
50
To see how progress, CLICK: FOLDER 1, then Folder 2, then Folder 3
51
QUESTION. What will happen as we take the limit as the change in x an y both tend to zero, which is taking the limit as we put in more and more rectangular boxes?
52
Answer.
Hide this folder from students.
53
All Done.
57
Ignore me. For the boundary of R (start with all clicked)