# What Is The Difference Between Left And Right Riemann Sum

The difference between a left and right Riemann sum is the way in which the rectangles that make up the area under the curve are placed. In a left Riemann sum, the rectangles are placed to the left of each sub-interval, while in a right Riemann sum, the rectangles are placed to the right of each sub-interval. This means that the left side of the rectangles always touch the curve in a left Riemann sum, while the right side of the rectangles always touch the curve in a right Riemann sum. As a result, the area under the curve is slightly larger or smaller depending on which type of Riemann sum is used.

The end points of the sub-intervals also differ depending on which type of Riemann sum is used. In a left Riemann sum, the end points of the sub-intervals lie on the left side of the sub-interval, while in a right Riemann sum, the end points of the sub-intervals lie on the right side of the sub-interval. This affects the accuracy of the sum as the end points may be either overestimating or underestimating the area under the curve.