Finding the area under a graph using Riemann Sum question
I would appreciate any help I can get with this problem! My prof usually gives us a few practice problems we should know. One of them this week was finding the area under the graph y=x^3 using Riemann Sum. Even in high school, I have had a hard time grasping how to find the area using Riemann Sum. I do not think it was explained to me right the first time.
Problem: find the area underneath the graph y=x^3 using eight subdivisions and rectangles underneath y.
The range is from 0 to 1
in my prof's example (of y=x^2) he used the following information:
the area of each rectangle is i^2/n^3 where i=(n-1)
so: [0^2]/n^3 + [1^2]/n^3 + [2^2]/n^3.... [(n-1)^2]/n^3
and because: [m(m+1)]/2=1+2+3...m
then: [0^2]/n^3 + [1^2]/n^3 + [2^2]/n^3.... [(n-1)^2]/n^3 = (n-1)(n)2n-1)/
I know that the above is confusing (at least in IMO) but I really would appreciate any guidance at all. Let me know if left any information out or was not clear enough