2 min readβ’december 17, 2021

A Riemann Sum estimates the area under a curve using rectangles. While this technique is not exact, it is an important tool that you can use if you are unable to differentiate or integrate an equation.Β **Need more help, check out this other ****study guide for Riemann Sum explanation and practice****!**

So imagine you are given this equation: f(x) = x^2. Your interval is [0,5] and n = 5. For the purposes of simplicity, I am going to demonstrate a Left Riemann Sum.

Equation: f(x) = x^2
Interval: [a,b] and in the case of this problem [1,5] - these are the parameters for the section under the curve that you are estimating
N: n=4 - this number determines how many rectangles you are splitting the section under the curve into. (Note: More rectangles = more precision, but also means more work)

(**If you were to take a Right Riemann Sum you would use the top right corner of each rectangle and if you were to use a Midpoint Riemann Sum the height would be where the middle of each rectangle hit the curve)

Our heights for this specific problem would be 1, 4, 9, and 16

(1)(1) + (1)(4) + (1)(9) + (1)(16) = 30Β

A =Β Ξx( f(x1) + f(x2) + f(x3)...)

^In simplest terms, this equation will help you solve any Riemann Sum. Note that all the steps are the same for Right Riemann Sums except for #3. Just remember to use the top left corner of your rectangles for each Left Riemann Sum and the top right corner for each Right Riemann Sum.Β

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