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Can you help me understand Riemann Sums in Si
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3/30/2015 10:47:26 PM
Posted: 2 years ago
Sorry if it's a bit wordy. I can't type all of the math symbols for you.
The Sigma notation is Sigma (with an non top and a k=1 at the bottom) followed by f(x superscripted with an asterisk and subscripted with k) multiplied by delta x.
The midpoint sum is the x superscripted to an asterisk and subscripted with k = a(the beginning point)+(k-1/2)delta x.
Say a is equal to 0, that is the big interval starts at a.
But then say you have a subinterval [0,1/2] and the change in x is 1/2. Then, the x value with super and subscripts is going to equal out to (1/2)k-1/4. Then for k=1/2 you get 1/4-1/4=0, so then you would be taking f(0) for that part of the summation. And I know it's supposed to be f(1/4) if it's a midpoint sum and you are taking it on the subinterval [1. 1/2].