Using a Riemman Sum to find the area under a curve (n intervals, left endpoint)

  • Thread starter tesla93
  • Start date
  • #1
23
0
Hello, I'm having a bit of trouble calculating the area under the curve of x^2 on the interval x=-3 to x=1. The question says that there I have to use n subintervals and left endpoints.

Relevant Equations

Δx=b-a/n

xi=a+(Δx)(i-1) -its i-1 because we're using a left endpoint, otherwise it would be just i.

f(xi)= (a+(Δx)(i-1))^2(Δx)

The Attempt


Δx=b-a/n
= 1-(-3)/n
=4/n

xi = -3+4/n(i-1)

f(xi)= (-3+4/n(i-1))^2(4/n)

=(9-(24i/n)+(24/n)+(16i^2/n^2)-(32i/n^2)-(16/n^2))*(4/n)

I got stuck at this point. I have no idea how to move on from here. Any advice?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

Related Threads on Using a Riemman Sum to find the area under a curve (n intervals, left endpoint)

Replies
1
Views
1K
Replies
0
Views
3K
  • Last Post
Replies
3
Views
4K
Replies
1
Views
4K
  • Last Post
Replies
2
Views
946
  • Last Post
Replies
19
Views
2K
  • Last Post
Replies
24
Views
814
Replies
1
Views
2K
  • Last Post
Replies
5
Views
12K
Top