- Thread starter
- #1

Ok, so i understand how to do this problem if it gave me an actual number of interval like n=6 but it doesn't and i'm not sure how to go about actually solving it without an actual number for n.

Thanks

- Thread starter ISITIEIW
- Start date

- Thread starter
- #1

Ok, so i understand how to do this problem if it gave me an actual number of interval like n=6 but it doesn't and i'm not sure how to go about actually solving it without an actual number for n.

Thanks

- Admin
- #2

- Mar 5, 2012

- 8,854

Welcome to MHB, ISITIEIW!

Ok, so i understand how to do this problem if it gave me an actual number of interval like n=6 but it doesn't and i'm not sure how to go about actually solving it without an actual number for n.

Thanks

I suggest you pick n equally spaced narrow rectangles numbered i = 1, ..., n.

To visualize it, you can start with n=6.

Then each rectangle will have width w=4/n.

For each rectangle we can pick an arbitrary coordinate $x_i$ between its left side and its right side. Say we pick the center, what would $x_i$ be then?

Substitute that $x_i$ in (x-2) and you get the height of each rectangle.

Can you calculate the sum of the areas of the rectangles?

And then let n go to infinity?