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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.

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Formulas:

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Video:

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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

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Examples:

1.)

Graph made from http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/riemann.html#instr

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2.)




Graph made from http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/riemann.html#instr

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3.)







Graph made from http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/riemann.html#instr

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4.)

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5.)



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

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Practice Links:

Practice right, left, and midpoint approximations
Left, right and trapezoidal riemann sums
Upper and lower riemann sums