Integrals & Sigma Notation

**rawkstar** · January 9th 2011, 07:38 PM

Consider the definite integral

Then the right Riemann sum obtained by subdividing the integral into

equal parts is

where

(Your answer should contain the variables

and

.) After simplifying this algebraically and breaking it up into three parts, we can write this Riemann sum as

where

should only depend on

and not on

. After applying the formulas

we can rewrite the Riemann sum as the following function of

:

Taking the limit of this as

, we obtain that

Im stuck at the first part. I know that the delta x is supposed to be b-a/n so that would be 2/n. other than that I am not sure where to go

**snowtea** · January 9th 2011, 08:41 PM

$f(x) = 3x^2 + 2x + 3$

Right Riemann sum in interval $[a,b]$ of $n$ equal parts is:
$\sum_{i=1}^n f(x_i)\Delta x$

Where $\Delta x = \frac{b-a}{n}$ and $x_i = a + i\Delta x$ .

**FernandoRevilla** · January 9th 2011, 08:53 PM

Also, this thread could be useful.

Fernando Revilla

Thread: Integrals & Sigma Notation

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