Right-endpoint approximation

Definition

Right-endpoint approximation is a method for estimating the definite integral of a function. It uses the value of the function at the right endpoint of each subinterval to create rectangles whose areas are summed.

5 Must Know Facts For Your Next Test

1. Right-endpoint approximation involves dividing the interval into equal subintervals.
2. The height of each rectangle is determined by the function's value at the right endpoint of each subinterval.
3. The sum of the areas of these rectangles approximates the area under the curve.
4. This method tends to overestimate or underestimate depending on whether the function is increasing or decreasing.
5. The formula for right-endpoint approximation is $R_n = \sum_{i=1}^n f(x_i)\Delta x$ where $x_i$ is the right endpoint and $\Delta x$ is the width of each subinterval.

Review Questions

• What determines the height of each rectangle in a right-endpoint approximation?
• When using right-endpoint approximation, what happens if a function is decreasing over an interval?
• How do you calculate $\Delta x$ when using right-endpoint approximation?

Related terms

Left-Endpoint Approximation: A method for estimating integrals using function values at the left endpoints of subintervals.

Midpoint Approximation: An estimation technique that uses function values at midpoints of subintervals.

Trapezoidal Rule:

A numerical method for approximating integrals by summing trapezoids formed under a curve.