SOLUTION: Problem: Find the midpoint riemann sum fro f(x) = cos(2x on the partition P = {-pi/6,0,pi/3,pi/2} from this if I understand correctly we would have to make an integral? &#8747;

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Question 1003527: Problem: Find the midpoint riemann sum fro f(x) = cos(2x on the partition P = {-pi/6,0,pi/3,pi/2}
from this if I understand correctly we would have to make an integral? ∫[from -pi/6 to pi/2]?
I think I understand Riemann sums. To find the midpoint sum we must take the two points of the subinterval then we halve them and we do this practice consecutively for all the provided sub-intervals then multiply the result of the halving and plug that into the original function and times the two together so it's A=B*H
I am having trouble seeing this one because I am not sure what the graph of cos(2x) looks like. Is it just a normal cosine graph? Does the 2 do anything special to the graph. Every time I do one of these Riemann sums I use the visual aid of the graph to find the midpoint sum but I can't seem to get the graph right. I attached an image to show what I have so far.
imgur.com/LsmX3Cf
Thank you!
Answer by ikleyn(52847) (Show Source):
You can put this solution on YOUR website!
.
From your plot in imgur.com/LsmX3Cf, it is difficult to understand which function is presented there.

Look in my plot below instead:

Plot of cos(2x) (in red) and cos(x) (in green)

Notice what the factor "2" at cos(2x) makes with the plot.

SOLUTION: Problem: Find the midpoint riemann sum fro f(x) = cos(2x on the partition P = {-pi/6,0,pi/3,pi/2} from this if I understand correctly we would have to make an integral? &#8747;

SOLUTION: Problem: Find the midpoint riemann sum fro f(x) = cos(2x on the partition P = {-pi/6,0,pi/3,pi/2} from this if I understand correctly we would have to make an integral? ∫