# How to Find a Formula for the Nth Right Endpoint Approximation

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Finding a formula for the Nth right endpoint approximation will require you to come up with a scheme for calculating the integral. Find a formula for the Nth right endpoint approximation with help from an experienced mathematics professional in this free video clip.

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## Video Transcript

Hello, my name is Walter Unglaub, and this is how to find a formula for the Nth right endpoint approximation. So the right endpoint approximation is an approximation scheme for calculating the integral or in other words the area underneath a curve. But could be described by say a function of x. So the integral, which would be the area underneath this curve from some point x initial to some point x final would be given in the continuum limit as the integral from x not to x final of f of x times dx. Here I have discritized the area underneath this curve using rectangles where the right endpoint is what's connecting to the actual continuous function. And the base or width of each of these rectangles is the same and it's going to be some constant non zero value delta x and so the area of say this rectangle would be delta x times my function evaluated at one, two, three, four because that's where the connection is made between the tip of the rectangle and the function. Four times delta x. So in general, the value of x is given as the number of rectangles times delta x and we can call that x sub n for short. So for a given rectangle the area of that rectangle would simply be equal to delta x times function evaluated at x of n. In this case I chose n to be equal to four. Therefore the area underneath the entire curve would be equal to a sum of the areas of each of these rectangles. So that area then can be approximated to the Nth rectangle or endpoint as the sum from n equals one to capital N which is the maximum number of rectangles and the approximation of delta x times the function evaluated at x sub n. And because this delta x is a constant and it does not depend on this lowercase n in the summation, then this can be simplified as delta x times the sum of little n going from one to big N of the function evaluated at that discreet point. My name is Walter Unglaub and this is how to find a formula for the Nth right endpoint approximation.

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