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

Below is the answer

http://img11.imageshack.us/img11/2533/img0057mb.th.jpg

Re: Quick Reimann Sum Question

$\displaystyle \{c_{i}\}$ is the set of points where you evaluate $\displaystyle f$ and $\displaystyle \Delta x_{i}=x_{i}-x_{i-1}$

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.

Re: Quick Reimann Sum Question

Do you know the geometric idea behind Riemann series? Basically the point is adding areas of rectangles, of height $\displaystyle f(c_{i})$ and width $\displaystyle \Delta x_{i}$. If you have the following sequence of points

$\displaystyle x_{0},x_{1},x_{2},x_{3},x_{4}$

you will have the following sequence of widths

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

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

$\displaystyle c_{1}=\frac{x_{1}-x_{0}}{2},c_{2}=\frac{x_{2}-x_{2}}{2},c_{3}=\frac{x_{2}-x_{1}}{2},c_{4}=\frac{x_{4}-x_{3}}{2}$

Re: Quick Reimann Sum Question

How do you know that Ci is midpoints thoe? Do you just assume it?

Re: Quick Reimann Sum Question

The Ci are the midpoints __by definition__.

Re: Quick Reimann Sum Question

Thanks,

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