Question

Explain Midpoint Riemann sum?
See below.

Answer 1

1. Use the given graph of f to find the Riemann sum with six subintervals. Take the sample points to be (a) left endpoints and (b) midpoints. In each case draw a diagram and
explain what the Riemann sum represents.

Answer 2

This is the work shown. I know how to do part (a), but I don't really understand part (b).

Answer 3

that was the wrong graph.

Answer 4

So for every Riemann sum you will divide up the graph into equal width intervals. The difference between the left, middle, and right hand sums are that the height is either the left, middle, or right side of the function on that interval.

Answer 5

ok, i get that.
but why is the first term 0.5? i understand that they add 1 each time, but where did the 0.5 come from?

Answer 6

That's because the first rectangle looks like this:



See how the height is halfway on the interval of each block?

Answer 7

.5 is midpoint of ( 0 + 1) /2 = ....

Answer 8

oh okay, thanks!