Write down the Riemann sum for int_2^3 2x dx using N equal subintervals, simplify, and find the limit as N approaches infinity.
I am not sure if I set the sum up properly and I am having trouble with the simplification. I don't really know what it is I am trying to isolate... N? i?
I am using the formula:
(b-a)/N Sigma_i=1^N [ f(a + i(b-a / N))]
so I have:
1/N Sigma_i=1 ^ N [ 2(2 + i(1/N))]
So where do I go from here? And also, when I take the limit as N approaches infinity, what do I do with terms including i?
Very helpful! Thank you!
So, is it safe to say that in taking the limit as N --> inf I can treat each N as a 1? I'm trying to see how taking the limit leads to 4 + 1...
I had thought that when the variable was in the denominator that term would equal 0...
The only way I see it leading to 4 + 1 is to have N = 1 but I'm just not sure if that's the correct thing to do. Clearly, I can see that the limit is 5 by looking at graph, but I was hoping to understand the algebra behind the concept. Thanks!