Question

Consider ∫R∫syDA, where R is the square R=[0,1]x[0,1]. Let us compute some Riemann sums. For any positive integer n we partition R into n^2 little squares Rij each with sides 1/n long. Within each little square we evaluate the integradn at the point (x*ij,y*ij), which is the upper right corner.

The first thing i'm having problems understanding with this problem is why that did it need to tell me that each square has an area of n^2 and that the lengths and width is 1/n long.

I have no problem calculating riemann sums if they let me pick how much I partition it myself or actually giving me a set number to partition them.

so if each side is 1/n long and the area of the squares is n^2 does that mean i can pick how to partition it as long as both ways i partition it (n and m) are equal?

also is there any deeper meaning to say that (x*ij,y*ij) are in the upper right corner or does that not even matter?

Answer 1

i meant ∫R∫xydA