Riemann sum facts for kids

Four of the Riemann summation methods for approximating the area under curves. Right and left methods make the approximation using the right and left endpoints of each subinterval, respectively. Maximum and minimum methods make the approximation using the largest and smallest endpoint values of each subinterval, respectively. The values of the sums converge as the subintervals halve from top-left to bottom-right.

In mathematics, a Riemann sum is a sum that makes an approximation of the total area underneath a curve on a graph. The area can be known as the integral. It may also be used to define the integration operation. The sum is named after a German mathematician who was called Bernhard Riemann.

Definition

You divide the horizontal length under the part of the function you want to evaluate into "n" equal pieces. That is the n on top of the Σ (Greek letter sigma). The (x_i-x_i-1) represents the size of one horizontal segment that is created from dividing the whole by the "n". The f(y_i) is a y value in an "n" segment. Since the area of a rectangle is length × width, the multiplication of x_i and f(y_i) is the area of a rectangle for that part of the graph. The Σ means we add up all of these small rectangles to get an approximation of the area under the segment of a function.

Images for kids

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  Left sum

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  Right sum

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  Middle sum

See also

In Spanish: Suma de Riemann para niños