# Reimann Sum Setup

• Nov 30th 2012, 07:13 AM
petenice
Reimann Sum Setup
Im having trouble setting up this Reimann Sum. The question is
Find the Riemann sum for f(x) = sin(x) over the interval [0, 2π],

where x0 = 0, x1 = π/4, x2 = π/3, x3 = π, and x4 = 2π, and

where c1 = π/6, c2 = π/3, c3 = 2π/3, and c4 = 3π/2. (Round your answer to three decimal places.)

So heres what i understand. n = 4, so there are 4 rectangles of uneven size. x0 - x4 are the given intervals.

I m guessing i should take $\sum_{i=1}^{n}$ $f(c_i)\Delta{x_i}$ and set it up like this $\sum_{n=0}^{2\pi}sin(c_i)\Delta{x_i}$.

But thats where im stuck. Do i evaluate each right end point times $\Delta{x_i}$ and add them up? Does $\Delta{x_i}$ = $\frac{2\pi}{n}i$ or $\frac{2\pi}{4}i$

Any help is greatly appreciated.
• Nov 30th 2012, 08:17 AM
Plato
Re: Reimann Sum Setup
Quote:

Originally Posted by petenice
I m guessing i should take $\sum_{i=1}^{n}$ $f(c_i)\Delta{x_i}$ and set it up like this $\sum_{n=0}^{2\pi}sin(c_i)\Delta{x_i}$.

You can do better than that.

$\sum\limits_{k = 1}^4 {\sin \left( {c_k } \right)\left( {x_k - x_{k - 1} } \right)}$