The process of finding the area under a particular curve by dividing the area into many tiny rectangles, adding up the heights of individual rectangles, and then multiplying the sum by their common width.

Formulas:

Video:

Steps:

1. Sketch the region
2. Establish whether f(x) is increasing/decreasing
- If increasing: Left rectangular approximation (LRAM) will be the LOWER sum (less than actual area) and Right rectangular approximation (RRAM) will
be the UPPER sum (greater than actual area)
- If decreasing: LRAM will be UPPER sum and RRAM will be LOWER sum
3. Determine the number of rectangles or trapezoids (n)
4. Find delta x
- Width of each rectangle
- Height of each trapezoid
5. Use formulas to solve for the estimated Area

## Table of Contents

## Definition:

The process of finding the area under a particular curve by dividing the area into many tiny rectangles, adding up the heights of individual rectangles, and then multiplying the sum by their common width.## Formulas:

## Video:

## Steps:

1. Sketch the region

2. Establish whether f(x) is increasing/decreasing

- If increasing: Left rectangular approximation (LRAM) will be the LOWER sum (less than actual area) and Right rectangular approximation (RRAM) will

be the UPPER sum (greater than actual area)

- If decreasing: LRAM will be UPPER sum and RRAM will be LOWER sum

3. Determine the number of rectangles or trapezoids (n)

4. Find

deltax- Width of each rectangle

- Height of each trapezoid

5. Use formulas to solve for the estimated Area

## Examples:

1.)Graph made from http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/riemann.html#instr2.)Graph made from http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/riemann.html#instr3.)Graph made from http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/riemann.html#instr4.)

5.)

http://www.calculus-help.com/probs1998/problem15.html## Practice Links:

Practice right, left, and midpoint approximations

Left, right and trapezoidal riemann sums

Upper and lower riemann sums