## You are here

Homeright hand rule

## Primary tabs

# right hand rule

The *right hand rule* for computing the Riemann integral $\displaystyle\int\limits_{a}^{b}f(x)\,dx$ is

$\int\limits_{a}^{b}f(x)\,dx=\lim_{{n\to\infty}}\sum_{{j=1}}^{n}f\left(a+j\left% (\frac{b-a}{n}\right)\right)\left(\frac{b-a}{n}\right).$ |

If the Riemann integral is considered as a measure of area under a curve, then the expressions $\displaystyle f\left(a+j\left(\frac{b-a}{n}\right)\right)$ represent the heights of the rectangles, and $\displaystyle\frac{b-a}{n}$ is the common width of the rectangles.

The Riemann integral can be approximated by using a definite value for $n$ rather than taking a limit. In this case, the partition is $\displaystyle\left\{\left[a,a+\frac{b-a}{n}\right),\dots,\left[a+\frac{(b-a)(n% -1)}{n},b\right]\right\}$, and the function is evaluated at the right endpoints of each of these intervals. Note that this is a special case of a right Riemann sum in which the $x_{j}$’s are evenly spaced.

## Mathematics Subject Classification

41-01*no label found*28-00

*no label found*26A42

*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections