Consider the function f(x) = -x^2/2 -8
In this problem you will calculate by using the definition
The summation inside the brackets is which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub-interval.
Calculate for on the interval and write your answer as a function of without any summation signs.
Okay, I can't seem to get the right answer for this one. Here's what I have done so far:
The distance in play here is from 0 to 4, so with n number of rectangles, each width should be 4/n. I replaced x with 4/n(i) and replaced dx with 4/n.
Since in this equation we have x^2, I end up with
-(4/n(i))^2 / 2 - 8 (4/n)
I can't use "i" in my answer so I substituted it with the special sum formula for i^2 which is n(n+1)(2n+1)/6
All together then, what I came to is
((-[(4^2/n^2)(n(n+1)(2n+1)/6)]/2) - 8 )(4/n)
sorry for all the parentheses.
I know that this answer is wrong but I have no idea where I went wrong.
Thank you for any help!!