# Thread: Find the area by taking the limit

1. ## Find the area by taking the limit

Hi

the graph is f(x) = x

between x = 0 and x = 1

n= 6 from the diagram

using the right reiman sum

1/6 ( f(1/6)+f(2/6)+f(3/6)+f(4/6)+f(5/6)+f(6/6)) = 1/6 (21/6) = 7/12

but the limit part confuses me

lim sum n i=1 (i/n2)(1/n) = sum n i=1 i^2/n^3
n-> infinity

1/n^3 sum n i=1 i^2 but then I don't know what I am suppose to do

I am following an example in my text and all of a sudden it becomes ns and I don't know what happened to "i"

Any enlightenment on what I am doing is greatly appreciated.

Thanks

this calculus beginner - the term is almost over and I still feel very much like a beginner....thanks for all of you experts who help us.

2. The area, since it's a triangle from (0,0) to (1,1), is .5.
I don't know where you're getting that Reimann sum from.
But that limit is 1/3.
I think you are integrating $x^2$ instead from (0,0) to (1,1), which has area 1/3.