Quick Reimann Sum Question

• Apr 3rd 2013, 03:22 PM
minneola24
Quick Reimann Sum Question
Hello,

My only question is what is the relation c# and x# and delta X

No need to solve it, I just need to know what the relationship is =) Thanks!!

Below is the question (ignore figure for 72)
you have to click it ;)

http://www.imageshack.us/thumbnail.png

http://img11.imageshack.us/img11/2533/img0057mb.th.jpg
• Apr 3rd 2013, 03:26 PM
Ruun
Re: Quick Reimann Sum Question
$\{c_{i}\}$ is the set of points where you evaluate $f$ and $\Delta x_{i}=x_{i}-x_{i-1}$
• Apr 3rd 2013, 03:28 PM
minneola24
Re: Quick Reimann Sum Question
Thanks for the quick response,

I understand Ci now, great.

But I am not sure how you are getting delta xi from just xi - xi-1

Could you please explain that part, thanks.
• Apr 3rd 2013, 03:34 PM
Ruun
Re: Quick Reimann Sum Question
Do you know the geometric idea behind Riemann series? Basically the point is adding areas of rectangles, of height $f(c_{i})$ and width $\Delta x_{i}$. If you have the following sequence of points

$x_{0},x_{1},x_{2},x_{3},x_{4}$
you will have the following sequence of widths

$\Delta x_{1}=x_{1}-x_{0},\Delta x_{2}=x_{2}-x_{1},\Delta x_{3}=x_{2}-x_{1},\Delta x_{4}=x_{3}-x_{2}$

and the following sequence of mid points $c_{i}$:

$c_{1}=\frac{x_{1}-x_{0}}{2},c_{2}=\frac{x_{2}-x_{2}}{2},c_{3}=\frac{x_{2}-x_{1}}{2},c_{4}=\frac{x_{4}-x_{3}}{2}$
• Apr 3rd 2013, 07:14 PM
minneola24
Re: Quick Reimann Sum Question
How do you know that Ci is midpoints thoe? Do you just assume it?
• Apr 3rd 2013, 07:29 PM
Gusbob
Re: Quick Reimann Sum Question
The Ci are the midpoints by definition.
• Apr 3rd 2013, 08:45 PM
minneola24
Re: Quick Reimann Sum Question
Thanks,

So then how do I tell if it wants a left / right or mid point?