Right-endpoint approximation

Definition

Right-endpoint approximation is a method to estimate the area under a curve by summing the areas of rectangles. The height of each rectangle is determined by the function value at the right endpoint of each subinterval.

5 Must Know Facts For Your Next Test

1. In right-endpoint approximation, the width of each rectangle is determined by dividing the interval into equal parts.
2. The formula for calculating an individual rectangle's area in this method is $f(x_i) \Delta x$, where $x_i$ is the right endpoint.
3. It tends to overestimate or underestimate depending on whether the function is increasing or decreasing.
4. The sum of all rectangular areas gives an estimate for the integral over the interval.
5. As you increase the number of subintervals, the approximation generally becomes more accurate.

Review Questions

• How do you determine the height of each rectangle in a right-endpoint approximation?
• Explain why increasing the number of subintervals improves the accuracy of a right-endpoint approximation.
• What happens to a right-endpoint approximation when applied to an increasing versus a decreasing function?

Related terms

Left-Endpoint Approximation: A method where rectangles are drawn with heights determined by function values at left endpoints of subintervals.

Midpoint Approximation: An approach that uses midpoints of subintervals to determine rectangle heights for estimating areas under curves.

Riemann Sum: A generalized method for approximating integrals using sums of rectangular areas based on various point selections within each subinterval.